  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 systems of type A we consider the Dunkl-type Riesz distributions,
prove that their Dunkl convolution exists and compute their convolution.
