Reproducing inversion formulas for the Dunkl-Wigner transforms

Fethi Soltani

doi:10.4067/S0719-06462015000200001

Reproducing inversion formulas for the Dunkl-Wigner transforms

Authors

Fethi Soltani Department of Mathematics, Faculty of Science, Jazan University, P.O.Box 277, Jazan 45142, Saudi Arabia

DOI:

https://doi.org/10.4067/S0719-06462015000200001

Keywords:

Dunkl transform, Dunkl-Wigner transform, inversion formulas, extremal functions

Abstract

We define and study the Fourier-Wigner transform associated with the Dunkl operators, and we prove for this transform a reproducing inversion formulas and a Plancherel formula. Next, we introduce and study the extremal functions associated to the Dunkl- Wigner transform.