Inversion Formulas for the Spherical Radon-Dunkl Transform

Abstract

The spherical Radon-Dunkl transform $R_{\kappa }$, associated to weight functions invariant under a finite reflection group, is introduced, and some elementary properties are obtained in terms of $h$-harmonics. Several inversion formulas of $R_{\kappa }$ are given with the aid of spherical Riesz-Dunkl potentials, the Dunkl operators, and some appropriate wavelet transforms.