Bulletin of the American Mathematical Society

MathSciNet review: 1567889
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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.

Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., 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, DOI 10.1007/BFb0072338

Mogens Flensted-Jensen, Discrete series for semisimple symmetric spaces, Ann. of Math. (2) 111 (1980), no. 2, 253–311. MR 569073, DOI 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, DOI 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 33421, DOI 10.2307/2372377

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, DOI 10.1007/978-1-4612-5298-6

Wilfried Schmid, Boundary value problems for group invariant differential equations, Astérisque Numéro Hors Série (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, DOI 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, DOI 10.1007/BF01474161

[CL] E. A. Coddington, N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955. MR 0069338




[D] M. Duflo, Lie group representations III, Lecture Notes in Math., vol. 1077, Springer-Verlag, Berlin, 1984, 100-165. MR 765553




[F] J. Flensted-Jensen, Discrete series for semisimple symmetric spaces, Ann. of Math. (2) 111 (1980), 253-311. MR 569073




[Ge] I. M. Gel'fand, Spherical functions in symmetric Riemannian spaces, Dokl. Akad. Nauk SSSR 70 (1950), 5-8. MR 33832




[He] S. Helgason, Groups and geometric analysis, Academic Press, New York, London, 1984. MR 754767




[HC] Harish-Chandra, Collected works, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1984.




[KK] M. Kashiwara, A. Kowata, K. Minemura, K. Okamoto, T. Oshima, and M. Tanaka, Eigenfunctions of invariant differential operators on symmetric spaces, Ann. of Math. (2) 107 (1978), 1-39. MR 485861




[Ko] K. 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 33421




[O] T. Oshima, Discrete series for semisimple symmetric spaces, Proceedings of the International Congress of Mathematicians, vol. 2, Polish Scientific Publishers-Warszawa and Elsevier Science Publishers, Amsterdam and New York, 1983, pp. 901-904. MR 804743




[S] H. Schlichtkrull, Hyperfunctions and harmonic analysis on symmetric spaces, Birkhäuser, Boston, 1984. MR 757178




[Sch] W. Schmid, Boundary value problems for group invariant differential equations, Astérisque, Elie Cartan et les Mathematiques d'aujourd'hui, 1983. MR 837206




[Wa] N. Wallach, Asymptotic expansions of generalized matrix entries of representations of real reductive groups, Representations of Lie groups I, Lecture Notes in Math., vol. 1024, Springer-Verlag, Berlin, 1983, pp. 287-369. MR 727854




[We] H. Weyl, Uber gewohnliche Differentialgleichungen mit Singularitaten und die zugehorigen Entwicklungen willkurlicher Funktionen, Math. Ann. 68 (1910), 220-269. MR 1511560