Fethi SOLTANI.Inversion Formula for the Dunkl-Wigner Transform and Compactness Property for the Dunkl-Weyl Transforms[J].数学研究及应用,2015,35(4):425~434
Inversion Formula for the Dunkl-Wigner Transform and Compactness Property for the Dunkl-Weyl Transforms
Inversion Formula for the Dunkl-Wigner Transform and Compactness Property for the Dunkl-Weyl Transforms
投稿时间:2015-01-21  最后修改时间:2015-04-27
DOI:10.3770/j.issn:2095-2651.2015.04.008
中文关键词:  Dunkl transform  Dunkl-Wigner transform  Dunkl-Weyl transforms  inversion formula  boundedness and compactness
英文关键词:Dunkl transform  Dunkl-Wigner transform  Dunkl-Weyl transforms  inversion formula  boundedness and compactness
基金项目:Supported by the DGRST Research Project LR11ES11 and CMCU Program 10G/1503.
作者单位
Fethi SOLTANI Department of Mathematics, Faculty of Science, Jazan University, P. O. Box 277, Jazan 45142, Saudi Arabia 
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中文摘要:
      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 $W_{\sigma}$ 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 $W_{\sigma}$.
英文摘要:
      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 $W_{\sigma}$ 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 $W_{\sigma}$.
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