Dunkl convolution and elliptic regularity for Dunkl operators

Abstract We discuss in which cases the Dunkl convolution of distributions , possibly both with non‐compact support, can be defined and study its analytic properties. We prove results on the (singular‐)support of Dunkl convolutions. Based on this, we are able to prove a theorem on elliptic regularity for a certain class of Dunkl operators, called elliptic Dunkl operators. Finally, for the root system we consider the Riesz distributions and prove that their Dunkl convolution exists and that holds.