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Inversion Formula for the Dunkl-Wigner Transform and Compactness Property for the Dunkl-Weyl Transforms
作者姓名:Fethi  SOLTANI
作者单位:Department of Mathematics, Faculty of Science, Jazan University, P. O. Box 277, Jazan 45142, Saudi Arabia
基金项目:Supported by the DGRST Research Project LR11ES11 and CMCU Program 10G/1503.
摘    要:We define and study the Fourier-Wigner transform associated with the Dunkl operators,and we prove for this transform an inversion formula.Next,we introduce and study the Weyl transforms W_σ associated with the Dunkl operators,where cr is a symbol in the Schwartz space S(R~d×R~d).An integral relation between the precedent Weyl and Wigner transforms is given.At last,we give criteria in terms of σ for boundedness and compactness of the transform W_σ.

关 键 词:Dunkl  transform    Dunkl-Wigner  transform    Dunkl-Weyl  transforms    inversion  formula    boundedness  and  compactness
收稿时间:2015/1/21 0:00:00
修稿时间:2015/4/27 0:00:00

Inversion Formula for the Dunkl-Wigner Transform and Compactness Property for the Dunkl-Weyl Transforms
Fethi SOLTANI.Inversion Formula for the Dunkl-Wigner Transform and Compactness Property for the Dunkl-Weyl Transforms[J].Journal of Mathematical Research with Applications,2015,35(4):425-434.
Authors:Fethi SOLTANI
Affiliation:Department of Mathematics, Faculty of Science, Jazan University, P. O. Box 277, Jazan 45142, Saudi Arabia
Abstract:We define and study the Fourier-Wigner transform associated with the Dunkl operators, and we prove for this transform an inversion formula. Next, we introduce and study the Weyl transforms $W_{\sigma}$ associated with the Dunkl operators, where $\sigma$ is a symbol in the Schwartz space $\mathcal{S}(\mathbb{R}^d\times\mathbb{R}^d)$. An integral relation between the precedent Weyl and Wigner transforms is given. At last, we give criteria in terms of $\sigma$ for boundedness and compactness of the transform $W_{\sigma}$.
Keywords:Dunkl transform  Dunkl-Wigner transform  Dunkl-Weyl transforms  inversion formula  boundedness and compactness
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