Dunkl positive definite functions

Abstract

We introduce the notion of Dunkl positive definite and strictly positive definite functions on ${\mathbb{R}}^d$. This done by the use of the properties of Dunkl translation. We establish the analogue of Bochner's theorem in Dunkl setting. The case of radial functions is considered. We give a sufficient condition for a function to be Dunkl strictly positive definite on ${\mathbb{R}}^d.$

arXiv comment18 pages