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Special Functions and Linear Representations of Lie Groups

About this Title

Jean Dieudonné

Publication: CBMS Regional Conference Series in Mathematics
Publication Year: 1980; Volume 42
ISBNs: 978-0-8218-1692-9 (print); 978-1-4704-2402-2 (online)
MathSciNet review: MR557540
MSC: Primary 22-02; Secondary 22E70, 33A75

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Table of Contents

Front/Back Matter


  • Introduction
  • Representations of SU(2)
  • The general theory of linear representations of compact groups
  • Lie theory of representations of compact connected Lie groups
  • Induced representations of compact groups
  • Spherical functions on compact groups
  • Examples; spherical harmonics
  • The general theory of spherical functions
  • Fourier and Plancherel transforms
  • Extension of the Plancherel transform
  • The subtleties of harmonic analysis
  • Differential properties of spherical functions on Lie groups
  • Spherical functions on semisimple Lie groups
  • More on SL(2, $\mathbb {R}$)
  • Automorphic functions
  • Groups of isometries and Bessel functions
  • Other special functions