Inversion Formulas for the Spherical Radon-Dunkl Transform

TL;DR

This paper introduces the spherical Radon-Dunkl transform, explores its properties using $h$-harmonics, and provides multiple inversion formulas leveraging Dunkl operators, wavelet transforms, and Riesz-Dunkl potentials.

Contribution

It presents new inversion formulas for the spherical Radon-Dunkl transform using advanced harmonic analysis tools.

Findings

Derived elementary properties of $R_$ in terms of $h$-harmonics

Established several inversion formulas for $R_$

Connected inversion formulas with Dunkl operators and wavelet transforms

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.