Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 5 (2009), 025, 15 pages      arXiv:0903.0573      http://dx.doi.org/10.3842/SIGMA.2009.025
Contribution to the Special Issue on Dunkl Operators and Related Topics

Inversion Formulas for the Spherical Radon-Dunkl Transform

Zhongkai Li and Futao Song
Department of Mathematics, Capital Normal University, Beijing 100048, China

Received October 18, 2008, in final form March 01, 2009; Published online March 03, 2009

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

Key words: spherical Radon-Dunkl transform; h-harmonics; inversion formula; wavelet.

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