Inversion Formulas for the Spherical Radon-Dunkl Transform

Abstract

The spherical Radon-Dunkl transform R_κ, 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_κ are given with the aid of spherical Riesz-Dunkl potentials, the Dunkl operators, and some appropriate wavelet transforms.

Keywords

• spherical Radon-Dunkl transform
• h-harmonics
• inversion formula
• wavelet