On the Generalized d’Alembert's and Wilson's Functional Equations on a Compact Group

Abstract

AbstractLet G be a compact group.Let σ be a continuous involution of G. In this paper, we are concerned by the following functional equationwhere f , g, h: G ⟼ ℂ, to be determined, are complex continuous functions on G such that f is central. This equation generalizes d’Alembert's and Wilson's functional equations. We show that the solutions are expressed by means of characters of irreducible, continuous and unitary representations of the group G.