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Mathematical Theory of Scattering Resonances
About this Title
Semyon Dyatlov, MIT, Cambridge, MA and Maciej Zworski, University of California, Berkeley, CA
Publication: Graduate Studies in Mathematics
Publication Year:
2019; Volume 200
ISBNs: 978-1-4704-4366-5 (print); 978-1-4704-5313-8 (online)
DOI: https://doi.org/10.1090/gsm/200
MathSciNet review: MR3969938
MSC: Primary 35P25; Secondary 34L25, 58J50, 81Q12, 81Q20, 81U20
Table of Contents
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Front/Back Matter
Chapters
Potential scattering
Geometric scattering
Resonances in the semiclassical limit
Appendices
- B. P. Abbott and et al., Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116 (2016), no. 6, 061102, 16. Authors include B. C. Barish, K. S. Thorne and R. Weiss. MR 3707758, DOI 10.1103/PhysRevLett.116.061102
- Shmuel Agmon, Spectral theory of Schrödinger operators on Euclidean and on non-Euclidean spaces, Comm. Pure Appl. Math. 39 (1986), no. S, suppl., S3–S16. Frontiers of the mathematical sciences: 1985 (New York, 1985). MR 861480, DOI 10.1002/cpa.3160390703
- Shmuel Agmon, A perturbation theory of resonances, Comm. Pure Appl. Math. 51 (1998), no. 11-12, 1255–1309. MR 1639212, DOI 10.1002/(SICI)1097-0312(199811/12)51:11/12<1255::AID-CPA2>3.3.CO;2-F
- J. Aguilar and J. M. Combes, A class of analytic perturbations for one-body Schrödinger Hamiltonians, Comm. Math. Phys. 22 (1971), 269–279. MR 345551
- Lars V. Ahlfors, Complex analysis, 3rd ed., International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., New York, 1978. An introduction to the theory of analytic functions of one complex variable. MR 510197
- Ivana Alexandrova and Hideo Tamura, Resonances in scattering by two magnetic fields at large separation and a complex scaling method, Adv. Math. 256 (2014), 398–448. MR 3177297, DOI 10.1016/j.aim.2014.01.022
- Serge Alinhac and Patrick Gérard, Pseudo-differential operators and the Nash-Moser theorem, Graduate Studies in Mathematics, vol. 82, American Mathematical Society, Providence, RI, 2007. Translated from the 1991 French original by Stephen S. Wilson. MR 2304160, DOI 10.1090/gsm/082
- M. F. Atiyah, R. Bott, and L. Gȧrding, Lacunas for hyperbolic differential operators with constant coefficients. I, Acta Math. 124 (1970), 109–189. MR 470499, DOI 10.1007/BF02394570
- Alain Bachelot and Agnès Motet-Bachelot, Les résonances d’un trou noir de Schwarzschild, Ann. Inst. H. Poincaré Phys. Théor. 59 (1993), no. 1, 3–68 (French, with English and French summaries). MR 1244181
- E. Balslev and J. M. Combes, Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions, Comm. Math. Phys. 22 (1971), 280–294. MR 345552
- C. Bardos, J.-C. Guillot, and J. Ralston, La relation de Poisson pour l’équation des ondes dans un ouvert non borné. Application à la théorie de la diffusion, Comm. Partial Differential Equations 7 (1982), no. 8, 905–958 (French). MR 668585, DOI 10.1080/03605308208820241
- C. Bardos, G. Lebeau, and J. Rauch, Scattering frequencies and Gevrey $3$ singularities, Invent. Math. 90 (1987), no. 1, 77–114. MR 906580, DOI 10.1007/BF01389032
- S. Barkhofen, T. Weich, A. Potzuweit, U. Kuhl, H.-J. Stöckmann, and M. Zworski, Experimental observation of spectral gap in microwave $n$-disk systems, Phys. Rev. Lett. 110 (2013), 164102.
- D. Baskin, An explicit description of the radiation field in $3+1$-dimensions, preprint, arXiv:1604.02984.
- Dean Baskin, Euan A. Spence, and Jared Wunsch, Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations, SIAM J. Math. Anal. 48 (2016), no. 1, 229–267. MR 3448345, DOI 10.1137/15M102530X
- Dean Baskin, András Vasy, and Jared Wunsch, Asymptotics of radiation fields in asymptotically Minkowski space, Amer. J. Math. 137 (2015), no. 5, 1293–1364. MR 3405869, DOI 10.1353/ajm.2015.0033
- Dean Baskin and Jared Wunsch, Resolvent estimates and local decay of waves on conic manifolds, J. Differential Geom. 95 (2013), no. 2, 183–214. MR 3128982
- M. C. Barr, M. P. Zaletel, and E. J. Heller, Quantum corral resonance widths: lossy scattering as acoustics, Nano Letters 10 (2010), 3253–3260.
- Matthew Bledsoe and Rudi Weikard, The inverse resonance problem for left-definite Sturm-Liouville operators, J. Math. Anal. Appl. 423 (2015), no. 2, 1753–1773. MR 3278226, DOI 10.1016/j.jmaa.2014.10.078
- Jean-Pierre Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 114 (1994), no. 2, 185–200. MR 1294924, DOI 10.1006/jcph.1994.1159
- D. Bindel and S. Govindjee, Elastic PMLs for resonator anchor loss simulations, Int. J. Num. Meth. Eng. 64 (2005), 789–818.
- D. Bindel and M. Zworski, Theory and computation of resonances in 1d scattering, http://www.cs.cornell.edu/\%7Ebindel/cims/resonant1d/
- M. Š. Birman and M. G. Kreĭn, On the theory of wave operators and scattering operators, Dokl. Akad. Nauk SSSR 144 (1962), 475–478 (Russian). MR 139007
- Jean-François Bony, Minoration du nombre de résonances engendrées par une trajectoire fermée, Comm. Partial Differential Equations 27 (2002), no. 5-6, 1021–1078 (French, with French summary). MR 1916556, DOI 10.1081/PDE-120004893
- Jean-François Bony, Vincent Bruneau, and Georgi Raikov, Counting function of characteristic values and magnetic resonances, Comm. Partial Differential Equations 39 (2014), no. 2, 274–305. MR 3169786, DOI 10.1080/03605302.2013.777453
- Jean-François Bony, Nicolas Burq, and Thierry Ramond, Minoration de la résolvante dans le cas captif, C. R. Math. Acad. Sci. Paris 348 (2010), no. 23-24, 1279–1282 (French, with English and French summaries). MR 2745339, DOI 10.1016/j.crma.2010.10.025
- J.-F. Bony, S. Fujiie, T. Ramond, and M. Zerzeri, Resonances for homoclinic trapped sets, Asterisque 405 (2018).
- Jean-François Bony and Dietrich Häfner, Decay and non-decay of the local energy for the wave equation on the de Sitter-Schwarzschild metric, Comm. Math. Phys. 282 (2008), no. 3, 697–719. MR 2426141, DOI 10.1007/s00220-008-0553-y
- Jean-François Bony and Johannes Sjöstrand, Traceformula for resonances in small domains, J. Funct. Anal. 184 (2001), no. 2, 402–418. MR 1851003, DOI 10.1006/jfan.2001.3771
- David Borthwick, Distribution of resonances for hyperbolic surfaces, Exp. Math. 23 (2014), no. 1, 25–45. MR 3177455, DOI 10.1080/10586458.2013.857282
- David Borthwick, Spectral theory of infinite-area hyperbolic surfaces, 2nd ed., Progress in Mathematics, vol. 318, Birkhäuser/Springer, [Cham], 2016. MR 3497464, DOI 10.1007/978-3-319-33877-4
- David Borthwick and Peter Perry, Scattering poles for asymptotically hyperbolic manifolds, Trans. Amer. Math. Soc. 354 (2002), no. 3, 1215–1231. MR 1867379, DOI 10.1090/S0002-9947-01-02906-3
- David Borthwick and Tobias Weich, Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions, J. Spectr. Theory 6 (2016), no. 2, 267–329. MR 3485944, DOI 10.4171/JST/125
- David Borthwick and Colin Guillarmou, Upper bounds for the number of resonances on geometrically finite hyperbolic manifolds, J. Eur. Math. Soc. (JEMS) 18 (2016), no. 5, 997–1041. MR 3500830, DOI 10.4171/JEMS/607
- David Borthwick and Tobias Weich, Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions, J. Spectr. Theory 6 (2016), no. 2, 267–329. MR 3485944, DOI 10.4171/JST/125
- Jean Bourgain and Semyon Dyatlov, Spectral gaps without the pressure condition, Ann. of Math. (2) 187 (2018), no. 3, 825–867. MR 3779959, DOI 10.4007/annals.2018.187.3.5
- Jean Bourgain, Alex Gamburd, and Peter Sarnak, Generalization of Selberg’s $\frac {3}{16}$ theorem and affine sieve, Acta Math. 207 (2011), no. 2, 255–290. MR 2892611, DOI 10.1007/s11511-012-0070-x
- Vincent Bruneau and Vesselin Petkov, Meromorphic continuation of the spectral shift function, Duke Math. J. 116 (2003), no. 3, 389–430. MR 1958093, DOI 10.1215/S0012-7094-03-11631-2
- Nicolas Burq, Décroissance de l’énergie locale de l’équation des ondes pour le problème extérieur et absence de résonance au voisinage du réel, Acta Math. 180 (1998), no. 1, 1–29 (French). MR 1618254, DOI 10.1007/BF02392877
- Nicolas Burq, Lower bounds for shape resonances widths of long range Schrödinger operators, Amer. J. Math. 124 (2002), no. 4, 677–735. MR 1914456
- Nicolas Burq, Semi-classical estimates for the resolvent in nontrapping geometries, Int. Math. Res. Not. 5 (2002), 221–241. MR 1876933, DOI 10.1155/S1073792802103059
- N. Burq, Smoothing effect for Schrödinger boundary value problems, Duke Math. J. 123 (2004), no. 2, 403–427 (English, with English and French summaries). MR 2066943, DOI 10.1215/S0012-7094-04-12326-7
- Nicolas Burq, Colin Guillarmou, and Andrew Hassell, Strichartz estimates without loss on manifolds with hyperbolic trapped geodesics, Geom. Funct. Anal. 20 (2010), no. 3, 627–656. MR 2720226, DOI 10.1007/s00039-010-0076-5
- Nicolas Burq and Maciej Zworski, Resonance expansions in semi-classical propagation, Comm. Math. Phys. 223 (2001), no. 1, 1–12. MR 1860756, DOI 10.1007/s002200100473
- V. S. Buslaev, Trace formulas for the Schrödinger operator in a three-dimensional space, Dokl. Akad. Nauk SSSR 143 (1962), 1067–1070 (Russian). MR 133691
- V. S. Buslaev, The asymptotic behavior of the spectral characteristics of exterior problems for the Schrödinger operator, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), 149–235, 240 (Russian). MR 364901
- Hui Cao and Jan Wiersig, Dielectric microcavities: model systems for wave chaos and non-Hermitian physics, Rev. Modern Phys. 87 (2015), no. 1, 61–111. MR 3400349, DOI 10.1103/RevModPhys.87.61
- F. Cardoso and G. Vodev, Uniform estimates of the resolvent of the Laplace-Beltrami operator on infinite volume Riemannian manifolds. II, Ann. Henri Poincaré 3 (2002), no. 4, 673–691. MR 1933365, DOI 10.1007/s00023-002-8631-8
- V. Cardoso, J. L. Costa, K. Destounis, P. Hintz, and A. Jansen, Quasinormal modes and strong cosmic censorship, Phys. Rev. Lett. 120 (2018), 031103.
- T. Carleman, Über die asymptotische Verteilung der Eigenwerte partieller Differentialgleichungen, Ber. Verk. Sächs. Akad. Wiss. Leipzig. Math.-Phys. Kl. 88 (1936), 119–134.
- T. Christiansen, Spectral asymptotics for compactly supported perturbations of the Laplacian on $\textbf {R}^n$, Comm. Partial Differential Equations 23 (1998), no. 5-6, 933–948. MR 1632784, DOI 10.1080/03605309808821373
- T. Christiansen, Some lower bounds on the number of resonances in Euclidean scattering, Math. Res. Lett. 6 (1999), no. 2, 203–211. MR 1689210, DOI 10.4310/MRL.1999.v6.n2.a8
- T. Christiansen, Schrödinger operators with complex-valued potentials and no resonances, Duke Math. J. 133 (2006), no. 2, 313–323. MR 2225694, DOI 10.1215/S0012-7094-06-13324-0
- T. Christiansen and P. D. Hislop, The resonance counting function for Schrödinger operators with generic potentials, Math. Res. Lett. 12 (2005), no. 5-6, 821–826. MR 2189242, DOI 10.4310/MRL.2005.v12.n6.a4
- T. J. Christiansen, Lower bounds for resonance counting functions for obstacle scattering in even dimensions, Amer. J. Math. 139 (2017), no. 3, 617–640. MR 3650228, DOI 10.1353/ajm.2017.0016
- T. J. Christiansen, A sharp lower bound for a resonance-counting function in even dimensions, Ann. Inst. Fourier (Grenoble) 67 (2017), no. 2, 579–604 (English, with English and French summaries). MR 3669507
- Yves Colin de Verdière, Une formule de traces pour l’opérateur de Schrödinger dans $\textbf {R}^{3}$, Ann. Sci. École Norm. Sup. (4) 14 (1981), no. 1, 27–39 (French). MR 618729
- Yves Colin de Verdière, Une nouvelle démonstration du prolongement méromorphe des séries d’Eisenstein, C. R. Acad. Sci. Paris Sér. I Math. 293 (1981), no. 7, 361–363 (French, with English summary). MR 639175
- Yves Colin de Verdière, Pseudo-laplaciens. II, Ann. Inst. Fourier (Grenoble) 33 (1983), no. 2, 87–113 (French). MR 699488
- Monique Combescure and Didier Robert, Coherent states and applications in mathematical physics, Theoretical and Mathematical Physics, Springer, Dordrecht, 2012. MR 2952171, DOI 10.1007/978-94-007-0196-0
- D. C. Clary, Spiers Memorial Lecture. Introductory lecture: quantum dynamics of chemical reactions, Faraday Discuss. 212 (2018), 9–32.
- M. F. Crommie, C. P. Lutz, and D. M. Eigler, Confinement of electrons to quantum corrals on a metal surface, Science 262 (1993), 218–220.
- Marzia Dalla Venezia and André Martinez, Widths of highly excited shape resonances, Ann. Henri Poincaré 18 (2017), no. 4, 1289–1304. MR 3626304, DOI 10.1007/s00023-017-0564-3
- Kiril Datchev, Local smoothing for scattering manifolds with hyperbolic trapped sets, Comm. Math. Phys. 286 (2009), no. 3, 837–850. MR 2472019, DOI 10.1007/s00220-008-0684-1
- Kiril Datchev, Quantitative limiting absorption principle in the semiclassical limit, Geom. Funct. Anal. 24 (2014), no. 3, 740–747. MR 3213828, DOI 10.1007/s00039-014-0273-8
- Kiril Datchev, Resonance free regions for nontrapping manifolds with cusps, Anal. PDE 9 (2016), no. 4, 907–953. MR 3530197, DOI 10.2140/apde.2016.9.907
- Kiril Datchev and Semyon Dyatlov, Fractal Weyl laws for asymptotically hyperbolic manifolds, Geom. Funct. Anal. 23 (2013), no. 4, 1145–1206. MR 3077910, DOI 10.1007/s00039-013-0225-8
- Kiril Datchev, Semyon Dyatlov, and Maciej Zworski, Resonances and lower resolvent bounds, J. Spectr. Theory 5 (2015), no. 3, 599–615. MR 3416834, DOI 10.4171/JST/108
- Kiril Datchev and András Vasy, Gluing semiclassical resolvent estimates via propagation of singularities, Int. Math. Res. Not. IMRN 23 (2012), 5409–5443. MR 2999147, DOI 10.1093/imrn/rnr255
- Kiril Datchev and András Vasy, Semiclassical resolvent estimates at trapped sets, Ann. Inst. Fourier (Grenoble) 62 (2012), no. 6, 2379–2384 (2013) (English, with English and French summaries). MR 3060761, DOI 10.5802/aif.2752
- E. B. Davies, Spectral theory and differential operators, Cambridge Studies in Advanced Mathematics, vol. 42, Cambridge University Press, Cambridge, 1995. MR 1349825, DOI 10.1017/CBO9780511623721
- Jean-Marc Delort, F.B.I. transformation, Lecture Notes in Mathematics, vol. 1522, Springer-Verlag, Berlin, 1992. Second microlocalization and semilinear caustics. MR 1186645, DOI 10.1007/BFb0095604
- Mouez Dimassi and Johannes Sjöstrand, Spectral asymptotics in the semi-classical limit, London Mathematical Society Lecture Note Series, vol. 268, Cambridge University Press, Cambridge, 1999. MR 1735654, DOI 10.1017/CBO9780511662195
- Mouez Dimassi and Maher Zerzeri, A local trace formula for resonances of perturbed periodic Schrödinger operators, J. Funct. Anal. 198 (2003), no. 1, 142–159. MR 1962356, DOI 10.1016/S0022-1236(02)00063-0
- Tien-Cuong Dinh and Duc-Viet Vu, Asymptotic number of scattering resonances for generic Schrödinger operators, Comm. Math. Phys. 326 (2014), no. 1, 185–208. MR 3162489, DOI 10.1007/s00220-013-1842-7
- T.-C. Dinh and V.-A. Nguyen, Distribution of scattering resonances for generic Schrödinger operators, arXiv:1709.06375.
- Shin-ichi Doi, Smoothing effects of Schrödinger evolution groups on Riemannian manifolds, Duke Math. J. 82 (1996), no. 3, 679–706. MR 1387689, DOI 10.1215/S0012-7094-96-08228-9
- Alexis Drouot, A quantitative version of Hawking radiation, Ann. Henri Poincaré 18 (2017), no. 3, 757–806. MR 3611016, DOI 10.1007/s00023-016-0509-2
- Alexis Drouot, Scattering resonances for highly oscillatory potentials, Ann. Sci. Éc. Norm. Supér. (4) 51 (2018), no. 4, 865–925 (English, with English and French summaries). MR 3861565, DOI 10.24033/asens.2368
- Alexis Drouot, Stochastic stability of Pollicott-Ruelle resonances, Comm. Math. Phys. 356 (2017), no. 2, 357–396. MR 3707328, DOI 10.1007/s00220-017-2956-0
- V. Duchêne, I. Vukićević, and M. I. Weinstein, Scattering and localization properties of highly oscillatory potentials, Comm. Pure Appl. Math. 67 (2014), no. 1, 83–128. MR 3139427, DOI 10.1002/cpa.21459
- Thomas Duyckaerts, Alain Grigis, and André Martinez, Resonance widths for general Helmholtz resonators with straight neck, Duke Math. J. 165 (2016), no. 14, 2793–2810. MR 3551774, DOI 10.1215/00127094-3644795
- Semyon Dyatlov, Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole, Comm. Math. Phys. 306 (2011), no. 1, 119–163. MR 2819421, DOI 10.1007/s00220-011-1286-x
- Semyon Dyatlov, Exponential energy decay for Kerr–de Sitter black holes beyond event horizons, Math. Res. Lett. 18 (2011), no. 5, 1023–1035. MR 2875874, DOI 10.4310/MRL.2011.v18.n5.a19
- Semyon Dyatlov, Asymptotic distribution of quasi-normal modes for Kerr–de Sitter black holes, Ann. Henri Poincaré 13 (2012), no. 5, 1101–1166. MR 2935116, DOI 10.1007/s00023-012-0159-y
- Semyon Dyatlov, Resonance projectors and asymptotics for $r$-normally hyperbolic trapped sets, J. Amer. Math. Soc. 28 (2015), no. 2, 311–381. MR 3300697, DOI 10.1090/S0894-0347-2014-00822-5
- Semyon Dyatlov, Asymptotics of linear waves and resonances with applications to black holes, Comm. Math. Phys. 335 (2015), no. 3, 1445–1485. MR 3320319, DOI 10.1007/s00220-014-2255-y
- Semyon Dyatlov, Spectral gaps for normally hyperbolic trapping, Ann. Inst. Fourier (Grenoble) 66 (2016), no. 1, 55–82 (English, with English and French summaries). MR 3477870
- S. Dyatlov, Improved fractal Weyl bounds for hyperbolic manifolds, with an appendix by D. Borthwick, S. Dyatlov, and T. Weich, J. Eur. Math. Soc. 21 (2019), 1595–1639.
- Semyon Dyatlov and Subhroshekhar Ghosh, Symmetry of bound and antibound states in the semiclassical limit for a general class of potentials, Proc. Amer. Math. Soc. 138 (2010), no. 9, 3203–3210. MR 2653945, DOI 10.1090/S0002-9939-2010-10519-1
- Semyon Dyatlov and Colin Guillarmou, Pollicott-Ruelle resonances for open systems, Ann. Henri Poincaré 17 (2016), no. 11, 3089–3146. MR 3556517, DOI 10.1007/s00023-016-0491-8
- Semyon Dyatlov and Long Jin, Resonances for open quantum maps and a fractal uncertainty principle, Comm. Math. Phys. 354 (2017), no. 1, 269–316. MR 3656519, DOI 10.1007/s00220-017-2892-z
- Semyon Dyatlov and Long Jin, Semiclassical measures on hyperbolic surfaces have full support, Acta Math. 220 (2018), no. 2, 297–339. MR 3849286, DOI 10.4310/ACTA.2018.v220.n2.a3
- Semyon Dyatlov and Joshua Zahl, Spectral gaps, additive energy, and a fractal uncertainty principle, Geom. Funct. Anal. 26 (2016), no. 4, 1011–1094. MR 3558305, DOI 10.1007/s00039-016-0378-3
- S. Dyatlov and M. Zworski, Trapping of waves and null geodesics for rotating black holes, Phys. Rev. D 88 (2013), 084037.
- Semyon Dyatlov and Maciej Zworski, Stochastic stability of Pollicott-Ruelle resonances, Nonlinearity 28 (2015), no. 10, 3511–3533. MR 3404148, DOI 10.1088/0951-7715/28/10/3511
- Semyon Dyatlov and Maciej Zworski, Dynamical zeta functions for Anosov flows via microlocal analysis, Ann. Sci. Éc. Norm. Supér. (4) 49 (2016), no. 3, 543–577 (English, with English and French summaries). MR 3503826, DOI 10.24033/asens.2290
- S. Dyatlov and M. Zworski, Fractal uncertainty for transfer operators, Int. Math. Res. Not. IMRN (2018), rny026, DOI 10.1093/imrn/rny026.
- L. Ermann, K. M. Frahm, and D. L. Shepelyansky, Google matrix analysis of directed networks, Rev. Mod. Phys. 87 (2015), 1261–1310.
- Lawrence C. Evans, Partial differential equations, Graduate Studies in Mathematics, vol. 19, American Mathematical Society, Providence, RI, 1998. MR 1625845, DOI 10.1090/gsm/019
- B. S. Pavlov and L. D. Faddeev, Scattering theory and automorphic functions, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 27 (1972), 161–193 (Russian). MR 320781
- Frédéric Faure and Masato Tsujii, Band structure of the Ruelle spectrum of contact Anosov flows, C. R. Math. Acad. Sci. Paris 351 (2013), no. 9-10, 385–391 (English, with English and French summaries). MR 3072166, DOI 10.1016/j.crma.2013.04.022
- John D. Fay, Fourier coefficients of the resolvent for a Fuchsian group, J. Reine Angew. Math. 293(294) (1977), 143–203. MR 506038, DOI 10.1515/crll.1977.293-294.143
- Charles Fefferman and C. Robin Graham, The ambient metric, Annals of Mathematics Studies, vol. 178, Princeton University Press, Princeton, NJ, 2012. MR 2858236
- Claudio Fernández and Richard Lavine, Lower bounds for resonance widths in potential and obstacle scattering, Comm. Math. Phys. 128 (1990), no. 2, 263–284. MR 1043521
- Richard Froese, Asymptotic distribution of resonances in one dimension, J. Differential Equations 137 (1997), no. 2, 251–272. MR 1456597, DOI 10.1006/jdeq.1996.3248
- R. Froese, P. Hislop, and P. Perry, The Laplace operator on hyperbolic three manifolds with cusps of nonmaximal rank, Invent. Math. 106 (1991), no. 2, 295–333. MR 1128217, DOI 10.1007/BF01243915
- Setsuro Fujiié, Amina Lahmar-Benbernou, and André Martinez, Width of shape resonances for non globally analytic potentials, J. Math. Soc. Japan 63 (2011), no. 1, 1–78. MR 2752432
- J. Galkowski, Distribution of resonances in scattering by thin barriers, arXiv:1404.3709.
- Jeffrey Galkowski, Resonances for thin barriers on the circle, J. Phys. A 49 (2016), no. 12, 125205, 22. MR 3465333, DOI 10.1088/1751-8113/49/12/125205
- Jeffrey Galkowski, A quantitative Vainberg method for black box scattering, Comm. Math. Phys. 349 (2017), no. 2, 527–549. MR 3594363, DOI 10.1007/s00220-016-2635-6
- Jeffrey Galkowski, The quantum Sabine law for resonances in transmission problems, Pure Appl. Anal. 1 (2019), no. 1, 27–100. MR 3900029, DOI 10.2140/paa.2019.1.27
- Jeffrey Galkowski and Hart F. Smith, Restriction bounds for the free resolvent and resonances in lossy scattering, Int. Math. Res. Not. IMRN 16 (2015), 7473–7509. MR 3428971, DOI 10.1093/imrn/rnu179
- Oran Gannot, From quasimodes to resonances: exponentially decaying perturbations, Pacific J. Math. 277 (2015), no. 1, 77–97. MR 3393682, DOI 10.2140/pjm.2015.277.77
- Oran Gannot, A global definition of quasinormal modes for Kerr-AdS black holes, Ann. Inst. Fourier (Grenoble) 68 (2018), no. 3, 1125–1167 (English, with English and French summaries). MR 3805770
- C. Robin Graham and Maciej Zworski, Scattering matrix in conformal geometry, Invent. Math. 152 (2003), no. 1, 89–118. MR 1965361, DOI 10.1007/s00222-002-0268-1
- Pierre Gaspard and Stuart A. Rice, Semiclassical quantization of the scattering from a classically chaotic repellor, J. Chem. Phys. 90 (1989), no. 4, 2242–2254. MR 980393, DOI 10.1063/1.456018
- C. Gérard, Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes, Mém. Soc. Math. France (N.S.) 31 (1988), 146 (French, with English summary). MR 998698
- C. Gérard and A. Martinez, Semiclassical asymptotics for the spectral function of long-range Schrödinger operators, J. Funct. Anal. 84 (1989), no. 1, 226–254. MR 999499, DOI 10.1016/0022-1236(89)90121-3
- C. Gérard, A. Martinez, and D. Robert, Breit-Wigner formulas for the scattering phase and the total scattering cross-section in the semi-classical limit, Comm. Math. Phys. 121 (1989), no. 2, 323–336. MR 985402
- C. Gérard and J. Sjöstrand, Semiclassical resonances generated by a closed trajectory of hyperbolic type, Comm. Math. Phys. 108 (1987), no. 3, 391–421. MR 874901
- C. Gérard and J. Sjöstrand, Resonances en limite semiclassique et exposants de Lyapunov, Comm. Math. Phys. 116 (1988), no. 2, 193–213 (French, with English summary). MR 939046
- P. Gérard, Mesures semi-classiques et ondes de Bloch, Séminaire sur les Équations aux Dérivées Partielles, 1990–1991, École Polytech., Palaiseau, 1991, pp. Exp. No. XVI, 19 (French). MR 1131589
- I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, RI, 1969. Translated from the Russian by A. Feinstein. MR 246142
- I. C. Gohberg and E. I. Sigal, An operator generalization of the logarithmic residue theorem and Rouché’s theorem, Mat. Sb. (N.S.) 84(126) (1971), 607–629 (Russian). MR 313856
- William L. Goodhue, Scattering theory for hyperbolic systems with coefficients of Gevrey type, Trans. Amer. Math. Soc. 180 (1973), 337–346. MR 415094, DOI 10.1090/S0002-9947-1973-0415094-5
- A. Goussev, R. Schubert, H. Waalkens, and S. Wiggins, Quantum theory of reactive scattering in phase space, Adv. Quant. Chem. 60 (2010), 269–332.
- C. Robin Graham and John M. Lee, Einstein metrics with prescribed conformal infinity on the ball, Adv. Math. 87 (1991), no. 2, 186–225. MR 1112625, DOI 10.1016/0001-8708(91)90071-E
- Alain Grigis and André Martinez, Resonance widths for the molecular predissociation, Anal. PDE 7 (2014), no. 5, 1027–1055. MR 3265958, DOI 10.2140/apde.2014.7.1027
- Alain Grigis and Johannes Sjöstrand, Microlocal analysis for differential operators, London Mathematical Society Lecture Note Series, vol. 196, Cambridge University Press, Cambridge, 1994. An introduction. MR 1269107, DOI 10.1017/CBO9780511721441
- Colin Guillarmou, Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds, Duke Math. J. 129 (2005), no. 1, 1–37. MR 2153454, DOI 10.1215/S0012-7094-04-12911-2
- Colin Guillarmou and Rafe Mazzeo, Resolvent of the Laplacian on geometrically finite hyperbolic manifolds, Invent. Math. 187 (2012), no. 1, 99–144. MR 2874936, DOI 10.1007/s00222-011-0330-y
- Victor Guillemin and Shlomo Sternberg, Semi-classical analysis, International Press, Boston, MA, 2013. MR 3157301
- L. Guillopé, Asymptotique de la phase de diffusion pour l’opérateur de Schrödinger dans $\textbf {R}^n$, Bony-Sjöstrand-Meyer seminar, 1984–1985, École Polytech., Palaiseau, 1985, pp. Exp. No. 5, 11 (French). MR 819771
- Laurent Guillopé, Kevin K. Lin, and Maciej Zworski, The Selberg zeta function for convex co-compact Schottky groups, Comm. Math. Phys. 245 (2004), no. 1, 149–176. MR 2036371, DOI 10.1007/s00220-003-1007-1
- Laurent Guillopé and Maciej Zworski, Upper bounds on the number of resonances for non-compact Riemann surfaces, J. Funct. Anal. 129 (1995), no. 2, 364–389. MR 1327183, DOI 10.1006/jfan.1995.1055
- Laurent Guillopé and Maciej Zworski, Polynomial bounds on the number of resonances for some complete spaces of constant negative curvature near infinity, Asymptotic Anal. 11 (1995), no. 1, 1–22. MR 1344252
- Laurent Guillopé and Maciej Zworski, Scattering asymptotics for Riemann surfaces, Ann. of Math. (2) 145 (1997), no. 3, 597–660. MR 1454705, DOI 10.2307/2951846
- L. Guillopé and M. Zworski, The wave trace for Riemann surfaces, Geom. Funct. Anal. 9 (1999), no. 6, 1156–1168. MR 1736931, DOI 10.1007/s000390050110
- Thierry Hargé and Gilles Lebeau, Diffraction par un convexe, Invent. Math. 118 (1994), no. 1, 161–196 (French). MR 1288472, DOI 10.1007/BF01231531
- W. K. Hayman, Subharmonic functions. Vol. 2, London Mathematical Society Monographs, vol. 20, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1989. MR 1049148
- Bernard Helffer, Semi-classical analysis for the Schrödinger operator and applications, Lecture Notes in Mathematics, vol. 1336, Springer-Verlag, Berlin, 1988. MR 960278, DOI 10.1007/BFb0078115
- Bernard Helffer, Spectral theory and its applications, Cambridge Studies in Advanced Mathematics, vol. 139, Cambridge University Press, Cambridge, 2013. MR 3027462
- B. Helffer and J. Sjöstrand, Résonances en limite semi-classique, Mém. Soc. Math. France (N.S.) 24-25 (1986), iv+228 (French, with English summary). MR 871788
- E. Heller, Quantum proximity resonances, Phys. Rev. Lett. 77 (1996), 4122–4125.
- Luc Hillairet and Chris Judge, Hyperbolic triangles without embedded eigenvalues, Ann. of Math. (2) 187 (2018), no. 2, 301–377. MR 3744854, DOI 10.4007/annals.2018.187.2.1
- Peter Hintz, Resonance expansions for tensor-valued waves on asymptotically Kerr–de Sitter spaces, J. Spectr. Theory 7 (2017), no. 2, 519–557. MR 3662017, DOI 10.4171/JST/171
- Peter Hintz and Andras Vasy, Non-trapping estimates near normally hyperbolic trapping, Math. Res. Lett. 21 (2014), no. 6, 1277–1304. MR 3335848, DOI 10.4310/MRL.2014.v21.n6.a5
- P. Hintz and A. Vasy, Global analysis of quasilinear wave equations on asymptotically Kerr-de Sitter spaces, arXiv:1404.1348.
- Peter Hintz and András Vasy, Semilinear wave equations on asymptotically de Sitter, Kerr–de Sitter and Minkowski spacetimes, Anal. PDE 8 (2015), no. 8, 1807–1890. MR 3441208, DOI 10.2140/apde.2015.8.1807
- Peter Hintz and András Vasy, The global non-linear stability of the Kerr–de Sitter family of black holes, Acta Math. 220 (2018), no. 1, 1–206. MR 3816427, DOI 10.4310/ACTA.2018.v220.n1.a1
- Peter Hintz and Maciej Zworski, Wave decay for star-shaped obstacles in $\Bbb R^3$: papers of Morawetz and Ralston revisited, Math. Proc. R. Ir. Acad. 117A (2017), no. 2, 47–62. MR 3697288, DOI 10.3318/pria.2017.117.06
- Peter Hintz and Maciej Zworski, Resonances for obstacles in hyperbolic space, Comm. Math. Phys. 359 (2018), no. 2, 699–731. MR 3783559, DOI 10.1007/s00220-017-3051-2
- Michael Hitrik and Iosif Polterovich, Resolvent expansions and trace regularizations for Schrödinger operators, Advances in differential equations and mathematical physics (Birmingham, AL, 2002) Contemp. Math., vol. 327, Amer. Math. Soc., Providence, RI, 2003, pp. 161–173. MR 1991539, DOI 10.1090/conm/327/05812
- M. W. Hirsch, C. C. Pugh, and M. Shub, Invariant manifolds, Lecture Notes in Mathematics, Vol. 583, Springer-Verlag, Berlin-New York, 1977. MR 501173
- P. D. Hislop and I. M. Sigal, Semiclassical theory of shape resonances in quantum mechanics, Mem. Amer. Math. Soc. 78 (1989), no. 399, 123. MR 989524, DOI 10.1090/memo/0399
- P. D. Hislop and I. M. Sigal, Introduction to spectral theory, Applied Mathematical Sciences, vol. 113, Springer-Verlag, New York, 1996. With applications to Schrödinger operators. MR 1361167, DOI 10.1007/978-1-4612-0741-2
- Justin Holmer and Maciej Zworski, Breathing patterns in nonlinear relaxation, Nonlinearity 22 (2009), no. 6, 1259–1301. MR 2507321, DOI 10.1088/0951-7715/22/6/002
- Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035, DOI 10.1007/978-3-642-96750-4
- Lars Hörmander, The analysis of linear partial differential operators. II, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 257, Springer-Verlag, Berlin, 1983. Differential operators with constant coefficients. MR 705278, DOI 10.1007/978-3-642-96750-4
- Lars Hörmander, The analysis of linear partial differential operators. III, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 274, Springer-Verlag, Berlin, 1985. Pseudodifferential operators. MR 781536
- Lars Hörmander, The analysis of linear partial differential operators. IV, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 275, Springer-Verlag, Berlin, 1985. Fourier integral operators. MR 781537
- W. Hunziker, Distortion analyticity and molecular resonance curves, Ann. Inst. H. Poincaré Phys. Théor. 45 (1986), no. 4, 339–358 (English, with French summary). MR 880742
- Mitsuru Ikawa, On the poles of the scattering matrix for two strictly convex obstacles, J. Math. Kyoto Univ. 23 (1983), no. 1, 127–194. MR 692733, DOI 10.1215/kjm/1250521614
- Mitsuru Ikawa, Decay of solutions of the wave equation in the exterior of several convex bodies, Ann. Inst. Fourier (Grenoble) 38 (1988), no. 2, 113–146 (English, with French summary). MR 949013
- Ahmed Intissar, A polynomial bound on the number of the scattering poles for a potential in even-dimensional spaces $\textbf {R}^n$, Comm. Partial Differential Equations 11 (1986), no. 4, 367–396. MR 829322, DOI 10.1080/03605308608820428
- Victor Ivrii, 100 years of Weyl’s law, Bull. Math. Sci. 6 (2016), no. 3, 379–452. MR 3556544, DOI 10.1007/s13373-016-0089-y
- T-C. Jagau, D. Zuev, K. B. Bravaya, E. Epifanovsky, and A. I. Krylov, A fresh look at resonances and complex absorbing potentials: density matrix-based approach, J. Phys. Chem. Lett. 5 (2014), 310–315.
- Dmitry Jakobson and Frédéric Naud, Lower bounds for resonances of infinite-area Riemann surfaces, Anal. PDE 3 (2010), no. 2, 207–225. MR 2657455, DOI 10.2140/apde.2010.3.207
- Dmitry Jakobson and Frédéric Naud, On the critical line of convex co-compact hyperbolic surfaces, Geom. Funct. Anal. 22 (2012), no. 2, 352–368. MR 2929068, DOI 10.1007/s00039-012-0154-y
- Dmitry Jakobson and Frédéric Naud, Resonances and density bounds for convex co-compact congruence subgroups of $SL_2(\Bbb {Z})$, Israel J. Math. 213 (2016), no. 1, 443–473. MR 3509479, DOI 10.1007/s11856-016-1332-7
- Arne Jensen, Spectral properties of Schrödinger operators and time-decay of the wave functions results in $L^{2}(\textbf {R}^{m})$, $m\geq 5$, Duke Math. J. 47 (1980), no. 1, 57–80. MR 563367
- Arne Jensen, Resonances in an abstract analytic scattering theory, Ann. Inst. H. Poincaré Sect. A (N.S.) 33 (1980), no. 2, 209–223. MR 605196
- Arne Jensen, Time-delay in potential scattering theory. Some “geometric” results, Comm. Math. Phys. 82 (1981/82), no. 3, 435–456. MR 641772
- Arne Jensen and Tosio Kato, Spectral properties of Schrödinger operators and time-decay of the wave functions, Duke Math. J. 46 (1979), no. 3, 583–611. MR 544248
- Arne Jensen and Gheorghe Nenciu, A unified approach to resolvent expansions at thresholds, Rev. Math. Phys. 13 (2001), no. 6, 717–754. MR 1841744, DOI 10.1142/S0129055X01000843
- Arne Jensen and Gheorghe Nenciu, The Fermi golden rule and its form at thresholds in odd dimensions, Comm. Math. Phys. 261 (2006), no. 3, 693–727. MR 2197544, DOI 10.1007/s00220-005-1428-0
- Long Jin, Resonance-free region in scattering by a strictly convex obstacle, Ark. Mat. 52 (2014), no. 2, 257–289. MR 3255140, DOI 10.1007/s11512-013-0185-0
- Long Jin, Scattering resonances of convex obstacles for general boundary conditions, Comm. Math. Phys. 335 (2015), no. 2, 759–807. MR 3317821, DOI 10.1007/s00220-014-2250-3
- Long Jin and Maciej Zworski, A local trace formula for Anosov flows, Ann. Henri Poincaré 18 (2017), no. 1, 1–35. With appendices by Frédéric Naud. MR 3592088, DOI 10.1007/s00023-016-0504-7
- J. A. Katine, M. A. Eriksson, A. S. Adourian, R. M. Westervelt, J. D. Edwards, A. Lupu-Sax, E. J. Heller, K. L. Campman, and A. C. Gossard, Point contact conductance of an open resonator, Phys. Rev. Lett. 79 (1997), 4806–4809.
- Tosio Kato, Perturbation theory for linear operators, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1980 edition. MR 1335452
- Frédéric Klopp and Maciej Zworski, Generic simplicity of resonances, Helv. Phys. Acta 68 (1995), no. 6, 531–538. MR 1395259
- Frédéric Klopp and Martin Vogel, Semiclassical resolvent estimates for bounded potentials, Pure Appl. Anal. 1 (2019), no. 1, 1–25. MR 3900028, DOI 10.2140/paa.2019.1.1
- Kostas D. Kokkotas and Bernd G. Schmidt, Quasi-normal modes of stars and black holes, Living Rev. Relativ. 2 (1999), 1999-2, 73. MR 1713080, DOI 10.12942/lrr-1999-2
- M. J. Körber, M. Michler, A. Bäcker, and R. Ketzmerick, Hierarchical fractal Weyl laws for chaotic resonance states in open mixed systems, Phys. Rev. Lett. 111 (2013), 114102.
- Evgeni Korotyaev, Stability for inverse resonance problem, Int. Math. Res. Not. 73 (2004), 3927–3936. MR 2104289, DOI 10.1155/S1073792804140609
- Evgeny Korotyaev, Inverse resonance scattering on the real line, Inverse Problems 21 (2005), no. 1, 325–341. MR 2146179, DOI 10.1088/0266-5611/21/1/020
- Evgeny Korotyaev, Lieb-Thirring type inequality for resonances, Bull. Math. Sci. 7 (2017), no. 2, 211–217. MR 3671735, DOI 10.1007/s13373-016-0092-3
- Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 217440
- Peter D. Lax and Ralph S. Phillips, Scattering theory for automorphic functions, Annals of Mathematics Studies, No. 87, Princeton University Press, Princeton, NJ, 1976. MR 562288
- Peter D. Lax and Ralph S. Phillips, The time delay operator and a related trace formula, Topics in functional analysis (essays dedicated to M. G. Kreĭn on the occasion of his 70th birthday), Adv. Math. Suppl. Stud., vol. 3, Academic Press, New York-London, 1978, pp. 197–215. MR 538021
- Peter D. Lax and Ralph S. Phillips, The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces, J. Functional Analysis 46 (1982), no. 3, 280–350. MR 661875, DOI 10.1016/0022-1236(82)90050-7
- G. Lebeau, Régularité Gevrey $3$ pour la diffraction, Comm. Partial Differential Equations 9 (1984), no. 15, 1437–1494 (French). MR 767870, DOI 10.1080/03605308408820368
- Minjae Lee and Maciej Zworski, A Fermi golden rule for quantum graphs, J. Math. Phys. 57 (2016), no. 9, 092101, 17. MR 3545219, DOI 10.1063/1.4961317
- B. Ja. Levin, Distribution of zeros of entire functions, Revised edition, Translations of Mathematical Monographs, vol. 5, American Mathematical Society, Providence, RI, 1980. Translated from the Russian by R. P. Boas, J. M. Danskin, F. M. Goodspeed, J. Korevaar, A. L. Shields and H. P. Thielman. MR 589888
- Kevin K. Lin, Numerical study of quantum resonances in chaotic scattering, J. Comput. Phys. 176 (2002), no. 2, 295–329. MR 1894769, DOI 10.1006/jcph.2001.6986
- Pierre-Louis Lions and Thierry Paul, Sur les mesures de Wigner, Rev. Mat. Iberoamericana 9 (1993), no. 3, 553–618 (French, with English and French summaries). MR 1251718, DOI 10.4171/RMI/143
- W. Lu, S. Sridhar, and M. Zworski, Fractal Weyl laws for chaotic open systems, Phys. Rev. Lett. 91 (2003), 154101.
- N. Mandouvalos, Spectral theory and Eisenstein series for Kleinian groups, Proc. London Math. Soc. (3) 57 (1988), no. 2, 209–238. MR 950590, DOI 10.1112/plms/s3-57.2.209
- A. S. Markus, Introduction to the spectral theory of polynomial operator pencils, Translations of Mathematical Monographs, vol. 71, American Mathematical Society, Providence, RI, 1988. Translated from the Russian by H. H. McFaden; Translation edited by Ben Silver; With an appendix by M. V. Keldysh. MR 971506, DOI 10.1090/mmono/071
- André Martinez, An introduction to semiclassical and microlocal analysis, Universitext, Springer-Verlag, New York, 2002. MR 1872698, DOI 10.1007/978-1-4757-4495-8
- A. Martinez, Resonance free domains for non globally analytic potentials, Ann. Henri Poincaré 3 (2002), no. 4, 739–756. MR 1933368, DOI 10.1007/s00023-002-8634-5
- Rafe Mazzeo, Unique continuation at infinity and embedded eigenvalues for asymptotically hyperbolic manifolds, Amer. J. Math. 113 (1991), no. 1, 25–45. MR 1087800, DOI 10.2307/2374820
- Rafe R. Mazzeo and Richard B. Melrose, Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature, J. Funct. Anal. 75 (1987), no. 2, 260–310. MR 916753, DOI 10.1016/0022-1236(87)90097-8
- Anders Melin, Operator methods for inverse scattering on the real line, Comm. Partial Differential Equations 10 (1985), no. 7, 677–766. MR 792566, DOI 10.1080/03605308508820393
- Richard Melrose, Scattering theory and the trace of the wave group, J. Functional Analysis 45 (1982), no. 1, 29–40. MR 645644, DOI 10.1016/0022-1236(82)90003-9
- R. B. Melrose, Growth estimates for the poles in potential scattering, unpublished manuscript, 1984.
- R. B. Melrose, Polynomial bounds on the distribution of poles in scattering by an obstacle, Journées “Équations aux Dérivées partielles”, Saint-Jean de Monts, 1984.
- Richard B. Melrose, Weyl asymptotics for the phase in obstacle scattering, Comm. Partial Differential Equations 13 (1988), no. 11, 1431–1439. MR 956828, DOI 10.1080/03605308808820582
- Richard B. Melrose, Spectral and scattering theory for the Laplacian on asymptotically Euclidian spaces, Spectral and scattering theory (Sanda, 1992) Lecture Notes in Pure and Appl. Math., vol. 161, Dekker, New York, 1994, pp. 85–130. MR 1291640
- Richard B. Melrose, Geometric scattering theory, Stanford Lectures, Cambridge University Press, Cambridge, 1995. MR 1350074
- Richard Melrose, Antônio Sá Barreto, and András Vasy, Analytic continuation and semiclassical resolvent estimates on asymptotically hyperbolic spaces, Comm. Partial Differential Equations 39 (2014), no. 3, 452–511. MR 3169792, DOI 10.1080/03605302.2013.866957
- R. B. Melrose and G. Uhlmann, An introduction to microlocal analysis, online book, http://www-math.mit.edu/~rbm/books/imaast.pdf
- M. Merkli and I. M. Sigal, A time-dependent theory of quantum resonances, Comm. Math. Phys. 201 (1999), no. 3, 549–576. MR 1685889, DOI 10.1007/s002200050568
- Christopher R. Moon, Laila S. Mattos, Brian K. Foster, Gabriel Zeltzer, Wonhee Ko, and Hari C. Manoharan, Quantum phase extraction in isospectral electronic nanostructures, Science 319 (2008), no. 5864, 782–787. MR 2385069, DOI 10.1126/science.1151490
- Cathleen S. Morawetz, The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961), 561–568. MR 132908, DOI 10.1002/cpa.3160140327
- Cathleen S. Morawetz, James V. Ralston, and Walter A. Strauss, Decay of solutions of the wave equation outside nontrapping obstacles, Comm. Pure Appl. Math. 30 (1977), no. 4, 447–508. MR 509770, DOI 10.1002/cpa.3160300405
- Minoru Murata, Asymptotic expansions in time for solutions of Schrödinger-type equations, J. Funct. Anal. 49 (1982), no. 1, 10–56. MR 680855, DOI 10.1016/0022-1236(82)90084-2
- Shu Nakamura, Plamen Stefanov, and Maciej Zworski, Resonance expansions of propagators in the presence of potential barriers, J. Funct. Anal. 205 (2003), no. 1, 180–205. MR 2020213, DOI 10.1016/S0022-1236(02)00112-X
- Frédéric Naud, Density and location of resonances for convex co-compact hyperbolic surfaces, Invent. Math. 195 (2014), no. 3, 723–750. MR 3166217, DOI 10.1007/s00222-013-0463-2
- Frédéric Naud, Bornes de Weyl fractales et résonances, Astérisque 390 (2017), Exp. No. 1107, 77–100 (French). Séminaire Bourbaki. Vol. 2015/2016. Exposés 1104–1119. MR 3666023
- L. Nedelec, Multiplicity of resonances in black box scattering, Canad. Math. Bull. 47 (2004), no. 3, 407–416. MR 2072601, DOI 10.4153/CMB-2004-040-7
- Roger G. Newton, Scattering theory of waves and particles, Dover Publications, Inc., Mineola, NY, 2002. Reprint of the 1982 second edition [Springer, New York; MR0666397 (84f:81001)], with list of errata prepared for this edition by the author. MR 1947260
- S. Nonnenmacher, Spectral problems in open quantum chaos, Nonlinearity 24 (2011), R123–R167.
- S. Nonnenmacher and E. Schenck, Resonance distribution in open quantum chaotic systems, Phys. Rev. E 78 (2008), 045202.
- Stéphane Nonnenmacher, Johannes Sjöstrand, and Maciej Zworski, From open quantum systems to open quantum maps, Comm. Math. Phys. 304 (2011), no. 1, 1–48. MR 2793928, DOI 10.1007/s00220-011-1214-0
- Stéphane Nonnenmacher, Johannes Sjöstrand, and Maciej Zworski, Fractal Weyl law for open quantum chaotic maps, Ann. of Math. (2) 179 (2014), no. 1, 179–251. MR 3126568, DOI 10.4007/annals.2014.179.1.3
- Stéphane Nonnenmacher and Maciej Zworski, Distribution of resonances for open quantum maps, Comm. Math. Phys. 269 (2007), no. 2, 311–365. MR 2274550, DOI 10.1007/s00220-006-0131-0
- Stéphane Nonnenmacher and Maciej Zworski, Quantum decay rates in chaotic scattering, Acta Math. 203 (2009), no. 2, 149–233. MR 2570070, DOI 10.1007/s11511-009-0041-z
- Stéphane Nonnenmacher and Maciej Zworski, Semiclassical resolvent estimates in chaotic scattering, Appl. Math. Res. Express. AMRX 1 (2009), 74–86. MR 2581379, DOI 10.1093/amrx/abp003
- Stéphane Nonnenmacher and Maciej Zworski, Decay of correlations for normally hyperbolic trapping, Invent. Math. 200 (2015), no. 2, 345–438. MR 3338007, DOI 10.1007/s00222-014-0527-y
- Hee Oh and Dale Winter, Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of $\textrm {SL}_2(\Bbb {Z})$, J. Amer. Math. Soc. 29 (2016), no. 4, 1069–1115. MR 3522610, DOI 10.1090/jams/849
- S. J. Patterson, Metaplectic forms and Gauss sums. I, Compositio Math. 62 (1987), no. 3, 343–366. MR 901396
- S. J. Patterson, The limit set of a Fuchsian group, Acta Math. 136 (1976), no. 3-4, 241–273. MR 450547, DOI 10.1007/BF02392046
- Peter A. Perry, The Laplace operator on a hyperbolic manifold. II. Eisenstein series and the scattering matrix, J. Reine Angew. Math. 398 (1989), 67–91. MR 998472, DOI 10.1515/crll.1989.398.67
- Vesselin Petkov and Luchezar Stoyanov, Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function, Anal. PDE 3 (2010), no. 4, 427–489. MR 2718260, DOI 10.2140/apde.2010.3.427
- Vesselin Petkov and Maciej Zworski, Breit-Wigner approximation and the distribution of resonances, Comm. Math. Phys. 204 (1999), no. 2, 329–351. MR 1704278, DOI 10.1007/s002200050648
- Vesselin Petkov and Maciej Zworski, Semi-classical estimates on the scattering determinant, Ann. Henri Poincaré 2 (2001), no. 4, 675–711. MR 1852923, DOI 10.1007/PL00001049
- R. S. Phillips and P. Sarnak, On cusp forms for co-finite subgroups of $\textrm {PSL}(2,\textbf {R})$, Invent. Math. 80 (1985), no. 2, 339–364. MR 788414, DOI 10.1007/BF01388610
- G. S. Popov, Asymptotics of Green’s functions in the shadow, C. R. Acad. Bulgare Sci. 38 (1985), no. 10, 1287–1290. MR 827840
- A. Potzuweit, T. Weich, S. Barkhofen, U. Kuhl, H.-J. Stöckmann, and M. Zworski, Weyl asymptotics: from closed to open systems, Phys. Rev. E. 86 (2012), 066205.
- G. R. Prony, Essai éxperimental et analytique: sur les lois de la dilatabilité, J. École Polytechnique, Floréal et Plairial, an III, 1 (1795), cahier 22, 24–76.
- James V. Ralston, Solutions of the wave equation with localized energy, Comm. Pure Appl. Math. 22 (1969), 807–823. MR 254433, DOI 10.1002/cpa.3160220605
- J. Ralston, Addendum to: “The first variation of the scattering matrix” (J. Differential Equations 21 (1976), no. 2, 378–394) by J. W. Helton and Ralston, J. Differential Equations 28 (1978), no. 1, 155–162. MR 481640, DOI 10.1016/0022-0396(78)90083-9
- Michael Reed and Barry Simon, Methods of modern mathematical physics. I, 2nd ed., Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. Functional analysis. MR 751959
- Michael Reed and Barry Simon, Methods of modern mathematical physics. III, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. Scattering theory. MR 529429
- T. Regge, Analytic properties of the scattering matrix, Nuovo Cimento (10) 8 (1958), 671–679. MR 95702
- W. P. Reinhardt, Complex Scaling in Atomic and Molecular Physics, In and Out of External Fields, Spectral theory and mathematical physics: a Festschrift in honor of Barry Simon’s 60th birthday, Proceedings of Symposia in Pure Mathematics, vol. 76, Amer. Math. Soc., Providence, RI, 2007, pp. 357–377.
- U. V. Riss and H. D. Meyer, Reflection-Free Complex Absorbing Potentials, J. Phys. B 28 (1995), 1475–1493.
- Didier Robert, Autour de l’approximation semi-classique, Progress in Mathematics, vol. 68, Birkhäuser Boston, Inc., Boston, MA, 1987 (French). MR 897108
- Igor Rodnianski and Terence Tao, Effective limiting absorption principles, and applications, Comm. Math. Phys. 333 (2015), no. 1, 1–95. MR 3294943, DOI 10.1007/s00220-014-2177-8
- Michel Rouleux, Absence of resonances for semiclassical Schrödinger operators with Gevrey coefficients, Hokkaido Math. J. 30 (2001), no. 3, 475–517. MR 1865424, DOI 10.14492/hokmj/1350912788
- Antonio Sá Barreto, Remarks on the distribution of resonances in odd dimensional Euclidean scattering, Asymptot. Anal. 27 (2001), no. 2, 161–170. MR 1852004
- Antônio Sá Barreto and Maciej Zworski, Existence of resonances in potential scattering, Comm. Pure Appl. Math. 49 (1996), no. 12, 1271–1280. MR 1414586, DOI 10.1002/(SICI)1097-0312(199612)49:12<1271::AID-CPA2>3.3.CO;2-I
- Antônio Sá Barreto and Maciej Zworski, Distribution of resonances for spherical black holes, Math. Res. Lett. 4 (1997), no. 1, 103–121. MR 1432814, DOI 10.4310/MRL.1997.v4.n1.a10
- W. Schlag, Dispersive estimates for Schrödinger operators: a survey, Mathematical aspects of nonlinear dispersive equations, Ann. of Math. Stud., vol. 163, Princeton Univ. Press, Princeton, NJ, 2007, pp. 255–285. MR 2333215
- R. Schubert, H. Waalkens, S. Wiggins, Efficient computation of transition state resonances and reaction rates from a quantum normal form, Phys. Rev. Lett. 96 (2006), 218302.
- Atle Selberg, Collected papers. Vol. I, Springer-Verlag, Berlin, 1989. With a foreword by K. Chandrasekharan. MR 1117906
- E. Servat, Résonances en dimension un pour l’opérateur de Schrödinger, Asymptot. Anal. 39 (2004), no. 3-4, 187–224 (French, with French summary). MR 2097993
- Jacob Shapiro, Semiclassical resolvent bounds in dimension two, Proc. Amer. Math. Soc. 147 (2019), no. 5, 1999–2008. MR 3937677, DOI 10.1090/proc/13758
- J. Shapiro, Semiclassical resolvent bound for compactly supported $L^\infty$ potentials, to appear in J. Spectr. Theory.
- Barry Simon, Quadratic form techniques and the Balslev-Combes theorem, Comm. Math. Phys. 27 (1972), 1–9. MR 321456
- Barry Simon, Resonances in $n$-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory, Ann. of Math. (2) 97 (1973), 247–274. MR 353896, DOI 10.2307/1970847
- B. Simon, The definition of molecular resonance curves by the method of exterior complex scaling, Phys. Lett. 71A (1979), 211–214.
- Barry Simon, Trace ideals and their applications, London Mathematical Society Lecture Note Series, vol. 35, Cambridge University Press, Cambridge-New York, 1979. MR 541149
- Barry Simon, Resonances in one dimension and Fredholm determinants, J. Funct. Anal. 178 (2000), no. 2, 396–420. MR 1802901, DOI 10.1006/jfan.2000.3669
- Johannes Sjöstrand, Singularités analytiques microlocales, Astérisque, 95, Astérisque, vol. 95, Soc. Math. France, Paris, 1982, pp. 1–166 (French). MR 699623
- Johannes Sjöstrand, Semiclassical resonances generated by nondegenerate critical points, Pseudodifferential operators (Oberwolfach, 1986) Lecture Notes in Math., vol. 1256, Springer, Berlin, 1987, pp. 402–429. MR 897789, DOI 10.1007/BFb0077753
- Johannes Sjöstrand, Geometric bounds on the density of resonances for semiclassical problems, Duke Math. J. 60 (1990), no. 1, 1–57. MR 1047116, DOI 10.1215/S0012-7094-90-06001-6
- J. Sjöstrand, A trace formula and review of some estimates for resonances, Microlocal analysis and spectral theory (Lucca, 1996) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 490, Kluwer Acad. Publ., Dordrecht, 1997, pp. 377–437. MR 1451399
- J. Sjöstrand, A trace formula for resonances and application to semi-classical Schrödinger operators, Séminaire sur les Équations aux Dérivées Partielles, 1996–1997, École Polytech., Palaiseau, 1997, pp. Exp. No. II, 17 (English, with French summary). MR 1482808
- J. Sjöstrand, Lectures on resonances, version préliminaire, printemps 2002.
- Johannes Sjöstrand, Weyl law for semi-classical resonances with randomly perturbed potentials, Mém. Soc. Math. Fr. (N.S.) 136 (2014), vi+144 (English, with English and French summaries). MR 3288114, DOI 10.24033/msmf.446
- Johannes Sjöstrand and Georgi Vodev, Asymptotics of the number of Rayleigh resonances, Math. Ann. 309 (1997), no. 2, 287–306. With an appendix by Jean Lannes. MR 1474193, DOI 10.1007/s002080050113
- Johannes Sjöstrand and Maciej Zworski, Complex scaling and the distribution of scattering poles, J. Amer. Math. Soc. 4 (1991), no. 4, 729–769. MR 1115789, DOI 10.1090/S0894-0347-1991-1115789-9
- Johannes Sjöstrand and Maciej Zworski, Lower bounds on the number of scattering poles, Comm. Partial Differential Equations 18 (1993), no. 5-6, 847–857. MR 1218521, DOI 10.1080/03605309308820953
- Johannes Sjöstrand and Maciej Zworski, Lower bounds on the number of scattering poles. II, J. Funct. Anal. 123 (1994), no. 2, 336–367. MR 1283032, DOI 10.1006/jfan.1994.1092
- Johannes Sjöstrand and Maciej Zworski, The complex scaling method for scattering by strictly convex obstacles, Ark. Mat. 33 (1995), no. 1, 135–172. MR 1340273, DOI 10.1007/BF02559608
- Johannes Sjöstrand and Maciej Zworski, Asymptotic distribution of resonances for convex obstacles, Acta Math. 183 (1999), no. 2, 191–253. MR 1738044, DOI 10.1007/BF02392828
- Johannes Sjöstrand and Maciej Zworski, Quantum monodromy and semi-classical trace formulae, J. Math. Pures Appl. (9) 81 (2002), no. 1, 1–33 (English, with English and French summaries). MR 1994881, DOI 10.1016/S0021-7824(01)01230-2
- Johannes Sjöstrand and Maciej Zworski, Fractal upper bounds on the density of semiclassical resonances, Duke Math. J. 137 (2007), no. 3, 381–459. MR 2309150, DOI 10.1215/S0012-7094-07-13731-1
- Johannes Sjöstrand and Maciej Zworski, Elementary linear algebra for advanced spectral problems, Ann. Inst. Fourier (Grenoble) 57 (2007), no. 7, 2095–2141 (English, with English and French summaries). Festival Yves Colin de Verdière. MR 2394537
- T. Seideman and W. H. Miller, Calculation of the cumulative reaction probability via a discrete variable representation with absorbing boundary conditions, J. Chem. Phys. 96 (1992), 4412–4422.
- Hart F. Smith and Maciej Zworski, Heat traces and existence of scattering resonances for bounded potentials, Ann. Inst. Fourier (Grenoble) 66 (2016), no. 2, 455–475 (English, with English and French summaries). MR 3477881
- A. Soffer and M. I. Weinstein, Time dependent resonance theory, Geom. Funct. Anal. 8 (1998), no. 6, 1086–1128. MR 1664792, DOI 10.1007/s000390050124
- P. D. Stefanov, Stability of resonances under smooth perturbations of the boundary, Asymptotic Anal. 9 (1994), no. 3, 291–296. MR 1295296
- Plamen Stefanov, Quasimodes and resonances: sharp lower bounds, Duke Math. J. 99 (1999), no. 1, 75–92. MR 1700740, DOI 10.1215/S0012-7094-99-09903-9
- Plamen Stefanov, Resonances near the real axis imply existence of quasimodes, C. R. Acad. Sci. Paris Sér. I Math. 330 (2000), no. 2, 105–108 (English, with English and French summaries). MR 1745179, DOI 10.1016/S0764-4442(00)00105-1
- Plamen Stefanov, Resonance expansions and Rayleigh waves, Math. Res. Lett. 8 (2001), no. 1-2, 107–124. MR 1825264, DOI 10.4310/MRL.2001.v8.n2.a2
- Plamen Stefanov, Approximating resonances with the complex absorbing potential method, Comm. Partial Differential Equations 30 (2005), no. 10-12, 1843–1862. MR 2182314, DOI 10.1080/03605300500300022
- Plamen Stefanov, Sharp upper bounds on the number of the scattering poles, J. Funct. Anal. 231 (2006), no. 1, 111–142. MR 2190165, DOI 10.1016/j.jfa.2005.07.007
- P. Stefanov and G. Vodev, Neumann resonances in linear elasticity for an arbitrary body, Comm. Math. Phys. 176 (1996), no. 3, 645–659. MR 1376435
- Dennis Sullivan, The density at infinity of a discrete group of hyperbolic motions, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 171–202. MR 556586
- Hideo Tamura, Aharonov-Bohm effect in resonances for scattering by three solenoids, Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 4, 45–49. MR 3327327, DOI 10.3792/pjaa.91.45
- Siu-Hung Tang and Maciej Zworski, From quasimodes to resonances, Math. Res. Lett. 5 (1998), no. 3, 261–272. MR 1637824, DOI 10.4310/MRL.1998.v5.n3.a1
- Siu-Hung Tang and Maciej Zworski, Resonance expansions of scattered waves, Comm. Pure Appl. Math. 53 (2000), no. 10, 1305–1334. MR 1768812, DOI 10.1002/1097-0312(200010)53:10<1305::AID-CPA4>3.3.CO;2-R
- S. H. Tang and M. Zworski, Potential scattering on the real line, unpublished notes, https://math.berkeley.edu/~zworski/tz1.pdf
- Michael E. Taylor, Partial differential equations I. Basic theory, 2nd ed., Applied Mathematical Sciences, vol. 115, Springer, New York, 2011. MR 2744150, DOI 10.1007/978-1-4419-7055-8
- Michael E. Taylor, Partial differential equations II. Qualitative studies of linear equations, 2nd ed., Applied Mathematical Sciences, vol. 116, Springer, New York, 2011. MR 2743652, DOI 10.1007/978-1-4419-7052-7
- E. C. Titchmarsh, The Zeros of Certain Integral Functions, Proc. London Math. Soc. (2) 25 (1926), 283–302. MR 1575285, DOI 10.1112/plms/s2-25.1.283
- E. C. Titchmarsh, The theory of functions, 2nd ed., Oxford University Press, Oxford, 1939. MR 3728294
- E. C. Titchmarsh, The theory of the Riemann zeta-function, 2nd ed., The Clarendon Press, Oxford University Press, New York, 1986. Edited and with a preface by D. R. Heath-Brown. MR 882550
- K. Uhlenbeck, Generic properties of eigenfunctions, Amer. J. Math. 98 (1976), no. 4, 1059–1078. MR 464332, DOI 10.2307/2374041
- B. R. Vaĭnberg, Exterior elliptic problems that depend polynomially on the spectral parameter, and the asymptotic behavior for large values of the time of the solutions of nonstationary problems, Mat. Sb. (N.S.) 92(134) (1973), 224–241, 343 (Russian). MR 346319
- B. R. \Vainberg, Asymptotic methods in equations of mathematical physics, Gordon and Breach, 1989.
- M. Vallisneri et al. The LIGO Open Science Center, Proceedings of the 10th LISA Symposium, University of Florida, Gainesville, May 18–23, 2014; arXiv:1410.4839.
- András Vasy, Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov), Invent. Math. 194 (2013), no. 2, 381–513. MR 3117526, DOI 10.1007/s00222-012-0446-8
- András Vasy, Microlocal analysis of asymptotically hyperbolic spaces and high-energy resolvent estimates, Inverse problems and applications: inside out. II, Math. Sci. Res. Inst. Publ., vol. 60, Cambridge Univ. Press, Cambridge, 2013, pp. 487–528. MR 3135765
- A. Vasy, Resolvent on Riemannian scattering (asymptotically conic) spaces, arXiv:1808.06123.
- András Vasy and Maciej Zworski, Semiclassical estimates in asymptotically Euclidean scattering, Comm. Math. Phys. 212 (2000), no. 1, 205–217. MR 1764368, DOI 10.1007/s002200000207
- Georgi Vodev, Sharp bounds on the number of scattering poles for perturbations of the Laplacian, Comm. Math. Phys. 146 (1992), no. 1, 205–216. MR 1163673
- Georgi Vodev, Sharp bounds on the number of scattering poles in even-dimensional spaces, Duke Math. J. 74 (1994), no. 1, 1–17. MR 1271461, DOI 10.1215/S0012-7094-94-07401-2
- Georgi Vodev, Sharp bounds on the number of scattering poles in the two-dimensional case, Math. Nachr. 170 (1994), 287–297. MR 1302380, DOI 10.1002/mana.19941700120
- Georgi Vodev, Exponential bounds of the resolvent for a class of noncompactly supported perturbations of the Laplacian, Math. Res. Lett. 7 (2000), no. 2-3, 287–298. MR 1764323, DOI 10.4310/MRL.2000.v7.n3.a4
- Georgi Vodev, Semi-classical resolvent estimates for Schrödinger operators, Asymptot. Anal. 81 (2013), no. 2, 157–170. MR 3059358
- Georgi Vodev, Semi-classical resolvent estimates and regions free of resonances, Math. Nachr. 287 (2014), no. 7, 825–835. MR 3207192, DOI 10.1002/mana.201300018
- G. Vodev, Semi-classical resolvent estimates for short-range $L^\infty$ potentials, Pure and Applied Analysis 1 (2019), 207–214.
- Claude M. Warnick, On quasinormal modes of asymptotically anti-de Sitter black holes, Comm. Math. Phys. 333 (2015), no. 2, 959–1035. MR 3296168, DOI 10.1007/s00220-014-2171-1
- M. Wei, G. Majda, and W. Strauss, Numerical computation of the scattering frequencies for acoustic wave equations, J. Comp. Phys. 75 (1988), 345–358.
- Calvin H. Wilcox, A generalization of theorems of Rellich and Atkinson, Proc. Amer. Math. Soc. 7 (1956), 271–276. MR 78912, DOI 10.1090/S0002-9939-1956-0078912-4
- Jared Wunsch and Maciej Zworski, Distribution of resonances for asymptotically Euclidean manifolds, J. Differential Geom. 55 (2000), no. 1, 43–82. MR 1849026
- Jared Wunsch and Maciej Zworski, Resolvent estimates for normally hyperbolic trapped sets, Ann. Henri Poincaré 12 (2011), no. 7, 1349–1385. MR 2846671, DOI 10.1007/s00023-011-0108-1
- D. R. Yafaev, Mathematical scattering theory, Translations of Mathematical Monographs, vol. 105, American Mathematical Society, Providence, RI, 1992. General theory; Translated from the Russian by J. R. Schulenberger. MR 1180965, DOI 10.1090/mmono/105
- D. R. Yafaev, Mathematical scattering theory, Mathematical Surveys and Monographs, vol. 158, American Mathematical Society, Providence, RI, 2010. Analytic theory. MR 2598115, DOI 10.1090/surv/158
- Maciej Zworski, Distribution of poles for scattering on the real line, J. Funct. Anal. 73 (1987), no. 2, 277–296. MR 899652, DOI 10.1016/0022-1236(87)90069-3
- Maciej Zworski, Sharp polynomial bounds on the number of scattering poles of radial potentials, J. Funct. Anal. 82 (1989), no. 2, 370–403. MR 987299, DOI 10.1016/0022-1236(89)90076-1
- Maciej Zworski, Sharp polynomial bounds on the number of scattering poles, Duke Math. J. 59 (1989), no. 2, 311–323. MR 1016891, DOI 10.1215/S0012-7094-89-05913-9
- M. Zworski, unpublished, 1990.
- M. Zworski, Counting scattering poles, Spectral and scattering theory (Sanda, 1992) Lecture Notes in Pure and Appl. Math., vol. 161, Dekker, New York, 1994, pp. 301–331. MR 1291649
- Maciej Zworski, Poisson formulae for resonances, Séminaire sur les Équations aux Dérivées Partielles, 1996–1997, École Polytech., Palaiseau, 1997, pp. Exp. No. XIII, 14. MR 1482819
- Maciej Zworski, Poisson formula for resonances in even dimensions, Asian J. Math. 2 (1998), no. 3, 609–617. MR 1724627, DOI 10.4310/AJM.1998.v2.n3.a6
- Maciej Zworski, Dimension of the limit set and the density of resonances for convex co-compact hyperbolic surfaces, Invent. Math. 136 (1999), no. 2, 353–409. MR 1688441, DOI 10.1007/s002220050313
- Maciej Zworski, A remark on isopolar potentials, SIAM J. Math. Anal. 32 (2001), no. 6, 1324–1326. MR 1856251, DOI 10.1137/S0036141000375585
- Maciej Zworski, Semiclassical analysis, Graduate Studies in Mathematics, vol. 138, American Mathematical Society, Providence, RI, 2012. MR 2952218, DOI 10.1090/gsm/138
- Maciej Zworski, Resonances for asymptotically hyperbolic manifolds: Vasy’s method revisited, J. Spectr. Theory 6 (2016), no. 4, 1087–1114. MR 3584195, DOI 10.4171/JST/153
- Maciej Zworski, Mathematical study of scattering resonances, Bull. Math. Sci. 7 (2017), no. 1, 1–85. MR 3625851, DOI 10.1007/s13373-017-0099-4