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 innite- dimensional Lie group C1 Rn ;GL n .

Keywords

• Spherical functions,Horn's series,SO p,q groups,de Sitter groups SO 4,1 and SO 3,2,conformal group SO 4,2,derivative of distribution

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