ON SOME HILBERT COSINE FUNCTIONS

Kinvi Kangni (Côte d’Ivoire), Saliou Toure (Côte d’Ivoire) and Ibrahima Toure (Côte d’Ivoire)

Received February 22, 2008

Abstract

We consider the equation: (1) in which a compact group K with normalized Haar measure dk acts on a locally compact group G by automorphism. Let H be a Hilbert space and be the bounded linear operators on H. Any bounded solution of (1) is called generalized cosine function. In this work we study some characterizations and properties of these cosine functions. The abelian case is developed by Stetkaer in [10].

Keywords and phrases: cosine function, Gelfand pair, Lie-spherical function, generalised Abel transformation.