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
Book Information:

Authors: R. Gangolli and V. S. Varadarajan
Title: Harmonic analysis of spherical functions on real reductive groups
Additional book information: Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 101, Springer-Verlag, Berlin, Heidelberg, and New York, 1988, xiv+365 pp., $110.00. ISBN 3-540-18302-7.

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

  • Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
  • Michel Duflo, On the Plancherel formula for almost algebraic real Lie groups, Lie group representations, III (College Park, Md., 1982/1983) Lecture Notes in Math., vol. 1077, Springer, Berlin, 1984, pp. 101–165. MR 765553, 10.1007/BFb0072338
  • Mogens Flensted-Jensen, Discrete series for semisimple symmetric spaces, Ann. of Math. (2) 111 (1980), no. 2, 253–311. MR 569073, 10.2307/1971201
  • I. M. Gel′fand, Spherical functions in symmetric Riemann spaces, Doklady Akad. Nauk SSSR (N.S.) 70 (1950), 5–8 (Russian). MR 0033832
  • Sigurdur Helgason, Groups and geometric analysis, Pure and Applied Mathematics, vol. 113, Academic Press, Inc., Orlando, FL, 1984. Integral geometry, invariant differential operators, and spherical functions. MR 754767
  • [HC] Harish-Chandra, Collected works, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1984.
  • M. Kashiwara, A. Kowata, K. Minemura, K. Okamoto, T. Ōshima, and M. Tanaka, Eigenfunctions of invariant differential operators on a symmetric space, Ann. of Math. (2) 107 (1978), no. 1, 1–39. MR 485861, 10.2307/1971253
  • Kunihiko Kodaira, The eigenvalue problem for ordinary differential equations of the second order and Heisenberg’s theory of 𝑆-matrices, Amer. J. Math. 71 (1949), 921–945. MR 0033421
  • Toshio Ōshima, Discrete series for semisimple symmetric spaces, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 901–904. MR 804743
  • Henrik Schlichtkrull, Hyperfunctions and harmonic analysis on symmetric spaces, Progress in Mathematics, vol. 49, Birkhäuser Boston, Inc., Boston, MA, 1984. MR 757178
  • Wilfried Schmid, Boundary value problems for group invariant differential equations, Astérisque Numero Hors Serie (1985), 311–321. The mathematical heritage of Élie Cartan (Lyon, 1984). MR 837206
  • Nolan R. Wallach, Asymptotic expansions of generalized matrix entries of representations of real reductive groups, Lie group representations, I (College Park, Md., 1982/1983) Lecture Notes in Math., vol. 1024, Springer, Berlin, 1983, pp. 287–369. MR 727854, 10.1007/BFb0071436
  • Hermann Weyl, Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen, Math. Ann. 68 (1910), no. 2, 220–269 (German). MR 1511560, 10.1007/BF01474161

Review Information:

Reviewer: D. Barbasch
Journal: Bull. Amer. Math. Soc. 23 (1990), 598-604
DOI: http://dx.doi.org/10.1090/S0273-0979-1990-15996-8