ZONAL AND ASSOCIATED FUNCTIONS ON SO0(p; q) GROUPS

B.A. RAJABOV

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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