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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)
DOI: https://doi.org/10.1090/cbms/042
MathSciNet review: MR557540
MSC: Primary 22-02; Secondary 22E70, 33A75
Table of Contents
Front/Back Matter
Chapters
- 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