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Book Review
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Book Information
Author(s):
Ricardo Estrada and Ram P. Kanwal
Title:
Asymptotic analysis. A distributional approach
Additional book information:
Birkhäuser,
Basel and Boston, MA,
1994,
ix + 258 pp.,
$49.50,
ISBN 0-8176-3716-8
References:
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- V. G. Avakumovi\'{c}: Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten. Math. Z. 65 (1956), 327-394. MR 18:316a
- [Ber]
- P. Bérard: Spectral geometry: direct and inverse problems. Lecture Notes in Mathematics 1207. Springer: Heidelberg 1986. MR 88f:58146
- [BeGaMa]
- M. Berger, P. Gauduchon, and E. Mazet, Le spectre d'une variété Riemannienne. Lecture Notes in Mathematics 194. Springer: Heidelberg 1971. MR 43:8025
- [BL]
- J. Brüning and M. Lesch: On the spectral geometry of algebraic curves. J. reine angewandte Math. 474 (1996), 25-66. MR 97d:58193
- [BS]
- J. Brüning and R. T. Seeley: Regular singular asymptotics. Adv. Math. 58 (1985), 133-148. MR 87b:41032
- [DG]
- H. Duistermaat and V. Guillemin: The spectrum of positive elliptic operators and periodic bicharacteristics. Inventiones math. 29 (1975), 39-79.
- [H]
- L. Hörmander: The spectral function of an elliptic operator. Acta Math. 121 (1968), 193-218. MR 58:29418
- [Ha]
- J. Hadamard: Lectures on Cauchy's problem in linear partial differential equations. Dover Publ.: New York 1952.
- [I]
- V. Ya. Ivrii: Second term of the spectral asymptotic expansion of the Laplace-Beltrami operator on manifolds with boundary. Functional Analysis Appl. 14 (1980), 98-106. MR 82m:58057
- [Je]
- H. Jeffreys: Asymptotic approximations. Clarendon Press; Oxford 1962. MR 26:5334
- [L]
- 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
- [McKS]
- H. P. Mckean and I. M. Singer: Curvature and the eigenvalues of the Laplacian. J. Diff. Geom. 1 (1967), 43-69. MR 36:828
- [MPl]
- 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
- [Mu]
- J. D. Murray: Asymptotic Analysis. Springer: Heidelberg 1984. MR 85m:34085
- [Ol]
- F. W. J. Olver: Asymptotics and special functions. Academic Press: New York 1974. MR 55:8655
- [OPS]
- B. Osgood, R. Phillips, and P. Sarnak: Compact isospectral sets of surfaces. J. Funct. Analysis 80 (1988), 212-234. MR 90d:58160
- [Ph]
- Pham The Lai: Meilleures estimations asymptotiques des restes de la fonction spectrale et des valeurs propres relatifs au laplacien. Math. Scand. 48 (1981), 5-38. MR 83b:35127a
- [S]
- R. T. Seeley: An estimate near the boundary for the spectral function of the Laplace operator. Am. J. Math. 102 (1980), 869-902. MR 82k:58097
- [W]
- H. Weyl: Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung). Math. Ann. 71 (1912), 441-479.
- [Wa]
- W. Wasow: Asymptotic expansions for ordinary differential equations. John Wiley: New York 1965. MR 34:3041
- [Wal]
- A. Walfisz: Gitterpunkte in mehrdimensionalen Kugeln. Monografie Matematyczne 33. Warschau 1957. MR 20:3826
- [WhWat]
- E. T. Whittacker and G. N. Watson: A course of modern analysis. Cambridge University Press: Cambridge 1965. MR 31:2375
Additional Information:
Reviewer(s):
Jochen
Brüning
Affiliation:
Humboldt-Universität zu Berlin, Institut für Mathematik
Email:
bruening@mathematik.hu-berlin.de
Review Information:
Journal:
Bull. Amer. Math. Soc.
35
(1998),
233-241.
MSC
(1991):
Primary 34E05
DOI:
10.1090/S0273-0979-98-00751-4
PII:
S 0273-0979(98)00751-4
Copyright of article:
Copyright
1998,
American Mathematical Society
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