Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
MathSciNet review:
4274519
Full text of review:
PDF
This review is available free of charge.
Book Information:
Authors:
S. Dyatlov and
M. Zworski
Title:
Mathematical theory of scattering resonances
Additional book information:
Graduate Studies in Mathematics, Vol. 200,
American Mathematical Society,
Providence, RI,
2019,
xi+634 pp.,
ISBN 978-1-4704-4366-5
David Borthwick, Spectral theory of infinite-area hyperbolic surfaces, Progress in Mathematics, vol. 256, Birkhäuser Boston, Inc., Boston, MA, 2007. MR 2344504, DOI 10.1007/978-0-8176-4653-0
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 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 Maciej Zworski, Ruelle zeta function at zero for surfaces, Invent. Math. 210 (2017), no. 1, 211–229. MR 3698342, DOI 10.1007/s00222-017-0727-3
Semyon Dyatlov and Maciej Zworski, Mathematical theory of scattering resonances, Graduate Studies in Mathematics, vol. 200, American Mathematical Society, Providence, RI, 2019. MR 3969938, DOI 10.1090/gsm/200
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 András Vasy, Stability of Minkowski space and polyhomogeneity of the metric, Ann. PDE 6 (2020), no. 1, Paper No. 2, 146. MR 4105742, DOI 10.1007/s40818-020-0077-0
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
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
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
References
- David Borthwick, Spectral theory of infinite-area hyperbolic surfaces, Progress in Mathematics, vol. 256, Birkhäuser Boston, Inc., Boston, MA, 2007. MR 2344504
- 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 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 Maciej Zworski, Ruelle zeta function at zero for surfaces, Invent. Math. 210 (2017), no. 1, 211–229. MR 3698342, DOI 10.1007/s00222-017-0727-3
- Semyon Dyatlov and Maciej Zworski, Mathematical theory of scattering resonances, Graduate Studies in Mathematics, vol. 200, American Mathematical Society, Providence, RI, 2019. MR 3969938, DOI 10.1090/gsm/200
- 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 András Vasy, Stability of Minkowski space and polyhomogeneity of the metric, Ann. PDE 6 (2020), no. 1, Paper No. 2, 146. MR 4105742, DOI 10.1007/s40818-020-0077-0
- 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
- András Vasy, Microlocal analysis of asymptotically hyperbolic and Kerr–de Sitter spaces, Invent. Math. 194 (2013), no. 2, 381–513. With an appendix by Semyon Dyatlov. MR 3117526, DOI 10.1007/s00222-012-0446-8
- 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
Review Information:
Reviewer:
Dean Baskin
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email:
dbaskin@math.tamu.edu
Journal:
Bull. Amer. Math. Soc.
58 (2021), 475-477
DOI:
https://doi.org/10.1090/bull/1714
Published electronically:
February 25, 2021
Review copyright:
© Copyright 2021
American Mathematical Society
