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Harmonic Analysis on Homogeneous Spaces

About this Title

Calvin C. Moore, Editor

Publication: Proceedings of Symposia in Pure Mathematics
Publication Year: 1973; Volume 26
ISBNs: 978-0-8218-1426-0 (print); 978-0-8218-9312-8 (online)
DOI: https://doi.org/10.1090/pspum/026

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Table of Contents

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Front/Back Matter

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Part I: Invited lectures

• Calvin C. Moore – Representations of solvable and nilpotent groups and harmonic analysis on nil and solvmanifolds [MR 0385001]
• V. S. Varadarajan – The theory of characters and the discrete series for semisimple Lie groups [MR 0409730]
• Sigurdur Helgason – Functions on symmetric spaces [MR 0346429]
• Robert J. Blattner – Quantization and representation theory [MR 0341529]
• Harish-Chandra – Harmonic analysis on reductive $p$-adic groups [MR 0340486]
• Harry Furstenberg – Boundary theory and stochastic processes on homogeneous spaces [MR 0352328]

Part II: Seminars

Seminar on representation theory of solvable groups and harmonic analysis on solvmanifolds (Chairman, L. Auslander)

• L. Pukanszky – The primitive ideal space of solvable Lie groups [MR 0333077]
• Adam Kleppner and Ronald L. Lipsman – Group extensions and the Plancherel formula [MR 0333065]
• Joseph A. Wolf and Calvin C. Moore – Square-integrable representations of nilpotent groups [MR 0333072]
• J. Brezin – Mackey’s little group method and $L^2$ of compact homogeneous spaces
• Roger Howe – On the spectrum of a compact solvmanifold [MR 0338264]
• H. Rossi and M. Vergne – Study of some holomorphically induced representations of solvable groups and restriction of the holomorphic discrete series of a semisimple group $G$ to the minimal parabolic of $G$ [MR 0338268]

Seminar on irreducibility and realization of various series of representations of semisimple groups (Chairman, B. Kostant)

• A. W. Knapp – Determination of intertwining operators [MR 0338266]
• Nolan R. Wallach – Kostant’s $P^\gamma$ and $R^\gamma$ matrices and intertwining integrals
• Kenneth Johnson – On an exceptional series of representations [MR 0340480]
• Takeshi Hirai – Explicit form of the characters of discrete series representations of semisimple Lie groups [MR 0404529]
• J. Lepowsky – The subquotient theorem and some applications [MR 0333073]
• P. C. Trombi – On the continuous spectrum for a semisimple Lie group [MR 0335690]
• Joseph A. Wolf – The spectrum of a reductive Lie group [MR 0369620]
• Joseph A. Wolf – Geometric realizations of representations of reductive Lie groups [MR 0369621]
• Leon Ehrenpreis – The use of partial differential equations for the study of group representations [MR 0344379]

Seminar on boundary behavior, special functions, and integral transforms in group representations (Chairman, E. Stein)

• Charles Fefferman – Some remarks on boundary behavior of analytic functions [MR 0419770]
• Lars-Ȧke Lindahl – Boundary behavior of Poisson integrals [MR 0333602]
• H. Lee Michelson – Generalized Poisson integrals and their boundary behavior [MR 0361629]
• Richard Askey – Refinements of Abel summability for Jacobi series [MR 0340934]
• M. Flensted-Jensen – Spherical functions on rank one symmetric spaces and generalizations [MR 0346430]
• Stephen Gelbart – Bessel functions, representation theory, and automorphic functions [MR 0344380]
• Kenneth I. Gross and Ray A. Kunze – Generalized Bessel transforms and unitary representations [MR 0344381]
• Tom Koornwinder – Explicit formulas for special functions related to symmetric spaces [MR 0346211]
• Willard Miller, Jr. – Lie algebras and generalizations of hypergeometric functions [MR 0335897]
• R. Strichartz – A noncompact analogue of spherical harmonics [MR 0344806]
• G. B. Folland – Subelliptic operators on the Heisenberg group [MR 0344700]
• E. M. Stein – Singular integrals related to nilpotent groups and $\bar \partial$ estimates [MR 0344701]
• Ronald R. Coifman and Guido Weiss – Operators transferred by representations of an amenable group [MR 0340967]
• Pierre Eymard – Invariant means and unitary representations [MR 0333064]

Seminar on representations of $p$-adic groups (Chairman, Harish-Chandra)

• Roger Howe – Two conjectures about reductive $p$-adic groups [MR 0338278]
• Hervé Jacquet – Zeta functions of simple algebras (local theory) [MR 0352056]
• Allan J. Silberger – On work of Macdonald and $L^2(G/B)$ for a $p$-adic group [MR 0338282]
• P. J. Sally, Jr. – Character formulas for $SL_2$ [MR 0338281]
• T. A. Springer – Characters of finite Chevalley groups [MR 0338150]
• Paul Gérardin – On the discrete series for Chevalley groups [MR 0367118]
• W. Casselman – The Steinberg character as a true character [MR 0338273]
• P. Cartier – Harmonic analysis on trees [MR 0338272]
• François Rodier – Whittaker models for admissible representations of reductive $p$-adic split groups [MR 0354942]

Seminar on automorphic forms and $L^2(G/\Gamma )$ (Chairman, R. Godement)

• Ramesh Gangolli – Spectra of discrete subgroups [MR 0367113]
• Stephen Gelbart – An example in the theory of automorphic forms [MR 0354558]
• Gilles Lachaud – Spectral analysis of automorphic forms on rank one groups by perturbation methods [MR 0338468]