ZONAL AND ASSOCIATED FUNCTIONS ON SO0 p; q GROUPS

Abstract

Explicit expressions for associated spherical functions of SO p; q matrix groups are obtained using a generalized hypergeometric series of two variables. In this paper we present explicit expressions for zonal functions of de Sitter groups and the group of conformal invariance. Moreover, we present a theorem on the transformation of derivative of distributions, concentrated on smooth surfaces, with respect to innite- dimensional Lie group C1 Rn ;GL n .