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 infinitedimensional Lie group C∞ (Rn, GL(n)).