On a mean value property associated with the dunkl laplacian operator and applications

Abstract

In this paper we are concerned with the Dunkl Laplacian Δ k on R d . We define a mean value property associated with Δ k . We prove that a function u defined on R d , satisfies the equation Δ ku= 0 if and only if it verifies a mean value property associated with the operator Δ k . Next we give some applications using this mean value.