American Mathematical Society

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, $49.50$

Cahit Arf, Untersuchungen über reinverzweigte Erweiterungen diskret bewerteter perfekter Körper, J. Reine Angew. Math. 181 (1939), 1–44 (German). MR 18, DOI 10.1515/crll.1940.181.1

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, DOI 10.1007/BFb0076330

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 10.1016/0001-8708(85)90114-8

[DG]

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 10.1007/BF02391913

[Ha]

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

Sam Perlis, Maximal orders in rational cyclic algebras of composite degree, Trans. Amer. Math. Soc. 46 (1939), 82–96. MR 15, DOI 10.1090/S0002-9947-1939-0000015-X

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

Morgan Ward and R. P. Dilworth, The lattice theory of ova, Ann. of Math. (2) 40 (1939), 600–608. MR 11, DOI 10.2307/1968944

J. D. Murray, Asymptotic analysis, 2nd ed., Applied Mathematical Sciences, vol. 48, Springer-Verlag, New York, 1984. MR 740864, DOI 10.1007/978-1-4612-1122-8

F. W. J. Olver, Asymptotics and special functions, Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1974. 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 10.1016/0022-1236(88)90071-7

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 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 10.2307/2374196

[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.

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