Softcover ISBN:  9780821816929 
Product Code:  CBMS/42 
59 pp 
List Price:  $21.00 
Individual Price:  $16.80 
Electronic ISBN:  9781470424022 
Product Code:  CBMS/42.E 
59 pp 
List Price:  $19.00 
Individual Price:  $15.20 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 42; 1980MSC: Primary 22; Secondary 33;

Table of Contents

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


Reviews

Presented in a clear, selfcontained, and wellorganized way, these introductory level lectures are highly recommended for individual or inclass use for acquiring basic knowledge of the groups \({\mathbf SU}(2)\), \({\mathbf SO}(3)\), \({\mathbf SL}(2, \mathbf R)\), and their function theories. Covering representations of \({\mathbf SU}(2)\), spherical harmonics on \(S_n\), representations of the group \({\mathbf SL}(2, \mathbf R)\) and spherical functions with respect to its maximal compact subgroup \({\mathbf SO}(2)\), these lectures also take account of some well known functions exhibited as spherical or matrixentry functions of unitary representations—for example, Jacobi polynomials and Legendre functions appear in this way for \({\mathbf SU}(2)\).
C. F. Dunkl, Mathematical Reviews


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 Book Details
 Table of Contents
 Reviews

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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

Presented in a clear, selfcontained, and wellorganized way, these introductory level lectures are highly recommended for individual or inclass use for acquiring basic knowledge of the groups \({\mathbf SU}(2)\), \({\mathbf SO}(3)\), \({\mathbf SL}(2, \mathbf R)\), and their function theories. Covering representations of \({\mathbf SU}(2)\), spherical harmonics on \(S_n\), representations of the group \({\mathbf SL}(2, \mathbf R)\) and spherical functions with respect to its maximal compact subgroup \({\mathbf SO}(2)\), these lectures also take account of some well known functions exhibited as spherical or matrixentry functions of unitary representations—for example, Jacobi polynomials and Legendre functions appear in this way for \({\mathbf SU}(2)\).
C. F. Dunkl, Mathematical Reviews