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 Wσ associated with the Dunk...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 Wσ associated with the Dunkl operators, where a is a symbol in the Schwartz space S（Rd × Rd）. 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 Wσ.展开更多
基金Supported by the DGRST Research Project LR11ES11 and CMCU Program 10G/1503
文摘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 Wσ associated with the Dunkl operators, where a is a symbol in the Schwartz space S（Rd × Rd）. 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 Wσ.
