Inversion Formulas for the Spherical Radon-Dunkl Transform

Zhongkai Li
2009 Symmetry, Integrability and Geometry: Methods and Applications  
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.
doi:10.3842/sigma.2009.025 fatcat:fe7hibou4regnnx5ofljiwymcq