CBMS Regional Conference Series in Mathematics 1980; 59 pp; softcover Number: 42 Reprint/Revision History: reprinted 1982 ISBN10: 0821816926 ISBN13: 9780821816929 List Price: US$19 Member Price: US$15.20 All Individuals: US$15.20 Order Code: CBMS/42
 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 representationsfor example, Jacobi polynomials and Legendre functions appear in this way for \({\mathbf SU}(2)\)."  C. F. Dunkl, Mathematical Reviews Table of Contents  Introduction
 Representations of \(\mathbf {SU}(2)\)
 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 \(\mathbf {SL}(2, \mathbf R)\)
 Automorphic functions
 Groups of isometries and Bessel functions
 Other special functions
 References
