Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Ricardo Estrada and Ram P. Kanwal
Title: Asymptotic analysis. A distributional approach
Additional book information: Birkhäuser, Basel and Boston, MA, 1994, ix + 258 pp., ISBN 0-8176-3716-8, $49.50$

References [Enhancements On Off] (What's this?)

    V. G. Avakumovi\'{c}: Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten. Math. Z. 65 (1956), 327-394. MR 18:316a
  • Pierre H. Bérard, Spectral geometry: direct and inverse problems, Lecture Notes in Mathematics, vol. 1207, Springer-Verlag, Berlin, 1986. With appendixes by Gérard Besson, and by Bérard and Marcel Berger. MR 861271
  • Marcel Berger, Paul Gauduchon, and Edmond Mazet, Le spectre d’une variété riemannienne, Lecture Notes in Mathematics, Vol. 194, Springer-Verlag, Berlin-New York, 1971 (French). MR 0282313
  • Jochen Brüning and Matthias Lesch, On the spectral geometry of algebraic curves, J. Reine Angew. Math. 474 (1996), 25–66. MR 1390691
  • Jochen Brüning and Robert Seeley, Regular singular asymptotics, Adv. in Math. 58 (1985), no. 2, 133–148. MR 814748, DOI https://doi.org/10.1016/0001-8708%2885%2990114-8
  • H. Duistermaat and V. Guillemin: The spectrum of positive elliptic operators and periodic bicharacteristics. Inventiones math. 29 (1975), 39-79.
  • Lars Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 193–218. MR 609014, DOI https://doi.org/10.1007/BF02391913
  • J. Hadamard: Lectures on Cauchy's problem in linear partial differential equations. Dover Publ.: New York 1952.
  • V. Ja. Ivriĭ, The second term of the spectral asymptotics for a Laplace-Beltrami operator on manifolds with boundary, Funktsional. Anal. i Prilozhen. 14 (1980), no. 2, 25–34 (Russian). MR 575202
  • Harold Jeffreys, Asymptotic approximations, Clarendon Press, Oxford, 1962. MR 0147821
  • B. M. Levitan: On the asymptotic behavior of the spectral function of a self-adjoint differential equation of second order. Izv. Akad. Nauk SSR ser. Mat. 16 (1952), 325-352. MR 15:315e
  • H. P. McKean Jr. and I. M. Singer, Curvature and the eigenvalues of the Laplacian, J. Differential Geometry 1 (1967), no. 1, 43–69. MR 217739
  • S. Minakshisundaram and Å. Pleijel: Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds. Canadian J. Math. 1 (1949), 242-256. MR 11:108b
  • J. D. Murray, Asymptotic analysis, 2nd ed., Applied Mathematical Sciences, vol. 48, Springer-Verlag, New York, 1984. MR 740864
  • F. W. J. Olver, Asymptotics and special functions, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Computer Science and Applied Mathematics. MR 0435697
  • B. Osgood, R. Phillips, and P. Sarnak, Compact isospectral sets of surfaces, J. Funct. Anal. 80 (1988), no. 1, 212–234. MR 960229, DOI https://doi.org/10.1016/0022-1236%2888%2990071-7
  • Phạm The Lại, Meilleures estimations asymptotiques des restes de la fonction spectrale et des valeurs propres relatifs au laplacien, Math. Scand. 48 (1981), no. 1, 5–38 (French). MR 621413, DOI https://doi.org/10.7146/math.scand.a-11895
  • R. Seeley, An estimate near the boundary for the spectral function of the Laplace operator, Amer. J. Math. 102 (1980), no. 5, 869–902. MR 590638, DOI https://doi.org/10.2307/2374196
  • H. Weyl: Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung). Math. Ann. 71 (1912), 441-479.
  • Wolfgang Wasow, Asymptotic expansions for ordinary differential equations, Pure and Applied Mathematics, Vol. XIV, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1965. MR 0203188
  • Arnold Walfisz, Gitterpunkte in mehrdimensionalen Kugeln, Monografie Matematyczne, Vol. 33, Państwowe Wydawnictwo Naukowe, Warsaw, 1957 (German). MR 0097357
  • E. T. Whittaker and G. N. Watson, A course of modern analysis. An introduction to the general theory of infinite processes and of analytic functions: with an account of the principal transcendental functions, Cambridge University Press, New York, 1962. Fourth edition. Reprinted. MR 0178117


Review Information:

Reviewer: Jochen Brüning
Affiliation: Humboldt-Universität zu Berlin, Institut für Mathematik
Email: bruening@mathematik.hu-berlin.de
Journal: Bull. Amer. Math. Soc. 35 (1998), 233-241
DOI: https://doi.org/10.1090/S0273-0979-98-00751-4
Review copyright: © Copyright 1998 American Mathematical Society