CBMS Regional Conference Series in Mathematics 1986; 77 pp; softcover Number: 61 ISBN10: 0821807110 ISBN13: 9780821807118 List Price: US$25 Member Price: US$20 All Individuals: US$20 Order Code: CBMS/61
 Harmonic analysis on Riemannian semisimple symmetric spaces and on special types of nonRiemannian semisimple symmetric spaces are wellestablished theories. This book presents a systematic treatment of the basic problems on semisimple symmetric spaces and a discussion of some of the more important recent developments in the field. The author's primary contribution has been his idea of how to construct the discrete series for such a space. In this book a fundamental role is played by the ideas behind that construction, namely the duality principle, the orbit picture related to it, and the definition of representations by means of distributions on the orbits. Intended as a text at the upper graduate level, the book assumes a basic knowledge of Fourier analysis, differential geometry, and functional analysis. In particular, the reader should have a good knowledge of the general theory of real and complex Lie algebras and Lie groups and of the root and weight theories for semisimple Lie algebras and Lie groups. Readership Table of Contents  Structure and classification of symmetric spaces
 Harmonic analysis on semisimple symmetric spaces
 The noncompact Riemannian form \(X^r\) of a semisimple symmetric space
 The Poisson transform on a symmetric space of noncompact type
 The \(H^d\)orbits on the boundary and the corresponding representation of \(G\)
 Representations related to the closed \(H^d\)orbits
 The discrete series for a semisimple symmetric space
