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

SIGMA 5 (2009), 071, 12 pages      arXiv:0907.2341      https://doi.org/10.3842/SIGMA.2009.071

Inversion of the Dual Dunkl-Sonine Transform on R Using Dunkl Wavelets

Mohamed Ali Mourou
Department of Mathematics, Faculty of Sciences, Al-Jouf University, P.O. Box 2014, Al-Jouf, Skaka, Saudi Arabia

Received March 02, 2009, in final form July 04, 2009; Published online July 14, 2009

Abstract
We prove a Calderón reproducing formula for the Dunkl continuous wavelet transform on R. We apply this result to derive new inversion formulas for the dual Dunkl-Sonine integral transform.

Key words: Dunkl continuous wavelet transform; Calderón reproducing formula; dual Dunkl-Sonine integral transform.

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