Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Strictly pseudoconvex domains in $C^n$
HTML articles powered by AMS MathViewer

by Michael Beals, Charles Fefferman and Robert Grossman PDF
Bull. Amer. Math. Soc. 8 (1983), 125-322
References
  • V. Arnold, Les mĂ©thodes mathĂ©matiques de la mĂ©canique classique, Éditions Mir, Moscow, 1976 (French). Traduit du russe par Djilali Embarek. MR 0474391
  • Steve Bell and Ewa Ligocka, A simplification and extension of Fefferman’s theorem on biholomorphic mappings, Invent. Math. 57 (1980), no. 3, 283–289. MR 568937, DOI 10.1007/BF01418930
  • Marcel Berger, Paul Gauduchon, and Edmond Mazet, Le spectre d’une variĂ©tĂ© riemannienne, Lecture Notes in Mathematics, Vol. 194, Springer-Verlag, Berlin-New York, 1971 (French). MR 0282313, DOI 10.1007/BFb0064643
  • L. Boutet de Monvel, IntĂ©gration des Ă©quations de Cauchy-Riemann induites formelles, SĂ©minaire Goulaouic-Lions-Schwartz 1974–1975; Équations aux derivĂ©es partielles linĂ©aires et non linĂ©aires, Exp. No. 9, Centre Math., École Polytech., Paris, 1975, pp. 14 (French). MR 0409893
  • L. Boutet de Monvel and J. Sjöstrand, Sur la singularitĂ© des noyaux de Bergman et de SzegƑ, JournĂ©es: Équations aux DĂ©rivĂ©es Partielles de Rennes (1975), AstĂ©risque, No. 34-35, Soc. Math. France, Paris, 1976, pp. 123–164 (French). MR 0590106
  • L. Boutet de Monvel, OpĂ©rateurs Ă  coefficients polynomiaux, espace de Bargmann, et opĂ©rateurs de Toeplitz, Goulaouic-Meyer-Schwartz Seminar, 1980–1981, École Polytech., Palaiseau, 1981, pp. Exp. No. II bis, 6 (French). MR 657971
  • 7. D. Burns and S. Schneider, personal communication. 8. E. Cartan, Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes. I, II, Oeuvres II, 2, 1231-1304; Oeuvres III, 2, 1217-1238. 9. D. Catlin, Necessary conditions for subellipticity and hypoellipticity for the ∂-Neumann problem on pseudoconvex domains, in [26].
  • Shiu Yuen Cheng and Shing Tung Yau, On the regularity of the Monge-AmpĂšre equation $\textrm {det}(\partial ^{2}u/\partial x_{i}\partial sx_{j})=F(x,u)$, Comm. Pure Appl. Math. 30 (1977), no. 1, 41–68. MR 437805, DOI 10.1002/cpa.3160300104
  • S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219–271. MR 425155, DOI 10.1007/BF02392146
  • Vladimir Grigorâ€Čevich Boltyanskii and Izrailâ€ČTsudikovich Gohberg, The decomposition of figures into smaller parts, Popular Lectures in Mathematics, University of Chicago Press, Chicago, Ill.-London, 1980. Translated from the Russian by Henry Christoffers and Thomas P. Branson. MR 563920
  • John P. D’Angelo, Orders of contact of real and complex subvarieties, Illinois J. Math. 26 (1982), no. 1, 41–51. MR 638553
  • 14. K. Diederich and P. Pflug, Necessary conditions for hypoellipticity of the $\bar \partial$-problem, in [26 ].
  • J. J. Duistermaat and V. W. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math. 29 (1975), no. 1, 39–79. MR 405514, DOI 10.1007/BF01405172
  • Michael Hitrik, Lagrangian tori and spectra for non-selfadjoint operators, SĂ©minaire: Équations aux DĂ©rivĂ©es Partielles. 2005–2006, SĂ©min. Équ. DĂ©riv. Partielles, École Polytech., Palaiseau, 2006, pp. Exp. No. XXIV, 16. Based on joint works with J. Sjöstrand and S. VĆ© Ngọc. MR 2276088
  • Ju. V. Egorov, Subelliptic pseudodifferential operators, Dokl. Akad. Nauk SSSR 188 (1969), 20–22 (Russian). MR 0255970
  • Ju. V. Egorov, The canonical transformations of pseudodifferential operators, Uspehi Mat. Nauk 24 (1969), no. 5 (149), 235–236 (Russian). MR 0265748
  • Ju. V. Egorov, Subelliptic operators, Uspehi Mat. Nauk 30 (1975), no. 2(182), 57–114 (Russian). MR 0410473
  • Ju. V. Egorov, Subelliptic operators, Uspehi Mat. Nauk 30 (1975), no. 3(183), 57–104 (Russian). MR 0410474
  • Charles Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1–65. MR 350069, DOI 10.1007/BF01406845
  • Charles L. Fefferman, Monge-AmpĂšre equations, the Bergman kernel, and geometry of pseudoconvex domains, Ann. of Math. (2) 103 (1976), no. 2, 395–416. MR 407320, DOI 10.2307/1970945
  • Charles Fefferman, Parabolic invariant theory in complex analysis, Adv. in Math. 31 (1979), no. 2, 131–262. MR 526424, DOI 10.1016/0001-8708(79)90025-2
  • G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Annals of Mathematics Studies, No. 75, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0461588
  • G. B. Folland and E. M. Stein, Estimates for the $\bar \partial _{b}$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429–522. MR 367477, DOI 10.1002/cpa.3160270403
  • Recent developments in several complex variables, Annals of Mathematics Studies, No. 100, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1981. Edited by John E. Fornaess. MR 627746
  • Peter B. Gilkey, The index theorem and the heat equation, Mathematics Lecture Series, No. 4, Publish or Perish, Inc., Boston, Mass., 1974. Notes by Jon Sacks. MR 0458504
  • Herbert Goldstein, Classical Mechanics, Addison-Wesley Press, Inc., Cambridge, Mass., 1951. MR 0043608
  • 29. R. Graham, to appear. 30. V. Guillemin, Some classical theorems in spectral theory revisited, in [35].
  • G. Hochschild and G. D. Mostow, Unipotent groups in invariant theory, Proc. Nat. Acad. Sci. U.S.A. 70 (1973), 646–648. MR 320174, DOI 10.1073/pnas.70.3.646
  • Lars Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. MR 222474, DOI 10.1007/BF02392081
  • Lars Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 193–218. MR 609014, DOI 10.1007/BF02391913
  • Lars Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79–183. MR 388463, DOI 10.1007/BF02392052
  • Lars Hörmander (ed.), Seminar on Singularities of Solutions of Linear Partial Differential Equations, Annals of Mathematics Studies, No. 91, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1979. Held at the Institute for Advanced Study, Princeton, N.J., 1977/78. MR 547013
  • 36. L. Hörmander, Subelliptic operators, in [35].
  • Norberto Kerzman, The Bergman kernel function. Differentiability at the boundary, Math. Ann. 195 (1972), 149–158. MR 294694, DOI 10.1007/BF01419622
  • 38. S. Kobayashi and K. Nomizu, Foundations of differential geometry, Wiley, New York, 1969. 39. J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds. I, II, Ann. of Math. (2) 78 (1963), 112-148; ibid 79 (1964), 450-472.
  • J. J. Kohn, Subellipticity of the $\bar \partial$-Neumann problem on pseudo-convex domains: sufficient conditions, Acta Math. 142 (1979), no. 1-2, 79–122. MR 512213, DOI 10.1007/BF02395058
  • Steven G. Krantz, Function theory of several complex variables, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1982. MR 635928
  • Masatake Kuranishi, Strongly pseudoconvex CR structures over small balls. I. An a priori estimate, Ann. of Math. (2) 115 (1982), no. 3, 451–500. MR 657236, DOI 10.2307/2007010
  • Serge Lang, Linear algebra, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1971. MR 0277543
  • 44. S. Lee and R. Melrose, personal communication. 45. V. P. Maslov, Theory of perturbations and asymptotic methods, Moskov. Gos. Univ., Moscow, 1965. (Russian)
  • Anders Melin and Johannes Sjöstrand, Fourier integral operators with complex-valued phase functions, Fourier integral operators and partial differential equations (Colloq. Internat., Univ. Nice, Nice, 1974) Lecture Notes in Math., Vol. 459, Springer, Berlin, 1975, pp. 120–223. MR 0431289
  • S. Minakshisundaram and Å. Pleijel, Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds, Canad. J. Math. 1 (1949), 242–256. MR 31145, DOI 10.4153/cjm-1949-021-5
  • JĂŒrgen Moser, Holomorphic equivalence and normal forms of hypersurfaces, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Part 2, Stanford Univ., Stanford, Calif., 1973) Amer. Math. Soc., Providence, R.I., 1975, pp. 109–112. MR 0435439
  • Alexander Nagel and E. M. Stein, Lectures on pseudodifferential operators: regularity theorems and applications to nonelliptic problems, Mathematical Notes, vol. 24, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1979. MR 549321
  • L. Nirenberg, A certain problem of Hans Lewy, Uspehi Mat. Nauk 29 (1974), no. 2(176), 241–251 (Russian). Translated from the English by Ju. V. Egorov; Collection of articles dedicated to the memory of Ivan Georgievič PetrovskiÄ­ (1901–1973), I. MR 0492752
  • L. Nirenberg, S. Webster, and P. Yang, Local boundary regularity of holomorphic mappings, Comm. Pure Appl. Math. 33 (1980), no. 3, 305–338. MR 562738, DOI 10.1002/cpa.3160330306
  • V. K. Patodi, Curvature and the eigenforms of the Laplace operator, J. Differential Geometry 5 (1971), 233–249. MR 292114, DOI 10.4310/jdg/1214429791
  • D. H. Phong, On integral representations for the Neumann operator, Proc. Nat. Acad. Sci. U.S.A. 76 (1979), no. 4, 1554–1558. MR 526179, DOI 10.1073/pnas.76.4.1554
  • Linda Preiss Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), no. 3-4, 247–320. MR 436223, DOI 10.1007/BF02392419
  • 55. M. Sato, T. Kawai and M. Kashiwera, Microfunctions and pseudodifferential equations, Lecture Notes in Math., vol. 287, Springer-Verlag, Berlin and New York, 1973.
  • C. S. Seshadri, On a theorem of Weitzenböck in invariant theory, J. Math. Kyoto Univ. 1 (1961/62), 403–409. MR 144914, DOI 10.1215/kjm/1250525012
  • Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
  • Noboru Tanaka, On the pseudo-conformal geometry of hypersurfaces of the space of $n$ complex variables, J. Math. Soc. Japan 14 (1962), 397–429. MR 145555, DOI 10.2969/jmsj/01440397
  • Noboru Tanaka, Graded Lie algebras and geometric structures, Proc. U.S.-Japan Seminar in Differential Geometry (Kyoto, 1965) Nippon Hyoronsha, Tokyo, 1966, pp. 147–150. MR 0222802
  • 60. D. S. Tartakoff, A survey of some recent results in C [26].
  • Michael E. Taylor, Pseudodifferential operators, Princeton Mathematical Series, No. 34, Princeton University Press, Princeton, N.J., 1981. MR 618463, DOI 10.1515/9781400886104
  • François TrĂšves, Analytic hypo-ellipticity of a class of pseudodifferential operators with double characteristics and applications to the $\overline \partial$-Neumann problem, Comm. Partial Differential Equations 3 (1978), no. 6-7, 475–642. MR 492802, DOI 10.1080/03605307808820074
  • François TrĂšves, Introduction to pseudodifferential and Fourier integral operators. Vol. 2, University Series in Mathematics, Plenum Press, New York-London, 1980. Fourier integral operators. MR 597145, DOI 10.1007/978-1-4684-8780-0
  • S. M. Webster, On the mapping problem for algebraic real hypersurfaces, Invent. Math. 43 (1977), no. 1, 53–68. MR 463482, DOI 10.1007/BF01390203
  • 65. R. Weizenböck, Über die invarianten von linearen gruppen, Acta Math. 58 (1932), 230-250.
  • R. O. Wells Jr., The Cauchy-Riemann equations and differential geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 2, 187–199. MR 640945, DOI 10.1090/S0273-0979-1982-14976-X
  • Hermann Weyl, The classical groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Their invariants and representations; Fifteenth printing; Princeton Paperbacks. MR 1488158
Similar Articles
  • Retrieve articles in Bulletin of the American Mathematical Society with MSC (1980): 32F15
  • Retrieve articles in all journals with MSC (1980): 32F15
Additional Information
  • Journal: Bull. Amer. Math. Soc. 8 (1983), 125-322
  • MSC (1980): Primary 32F15
  • DOI: https://doi.org/10.1090/S0273-0979-1983-15087-5
  • MathSciNet review: 684898