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 修订日期: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. |
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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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