Inversion Formulas for the Spherical Radon–Dunkl Transform

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.