Mean-periodic functions associated with the Dunkl operators

Abstract

In this work, we consider the Dunkl operator on the real line , defined for by A C ∞-function f on , is said to be mean-periodic function associated with the Dunkl operator 𝒟 k if there exists a nonzero distribution μ on with compact support such that where * k denotes the convolution associated with the Dunkl operator 𝒟 k . We characterize the solutions of these equations and we study the expansion of a mean-periodic function in series with respect to appropriate exponential monomials. Finally, we give some applications.