Time–frequency analysis associated with the generalized Wigner transform

Spectral theorems for Wigner transform associated with the Laguerre-Bessel localization operators

“…The theory of localization operators associated with the Fourier-Wigner transform has been studied and known remarkable development in many settings for example in the Riemann-Liouville setting [11],in the spherical mean setting [12],in the Laguerre setting [13],in the Dunkl setting [14],in the Weinstein setting [17],in the Heckman-Opdam-Jacobi setting [1],so its natural to ask whether there exists the equivalent of the theory of localization operators in other setting as the Laguerre Bessel setting. Following Wong's point of view,our main aim in this paper is to prove the analogues of the results on the localization operators studies by the authors in [1], [11], [12], [13], [14], [17] in the Laguerre-Bessel frame.…”

“…The theory of localization operators associated with the Fourier-Wigner transform has been studied and known remarkable development in many settings for example in the Riemann-Liouville setting [11],in the spherical mean setting [12],in the Laguerre setting [13],in the Dunkl setting [14],in the Weinstein setting [17],in the Heckman-Opdam-Jacobi setting [1],so its natural to ask whether there exists the equivalent of the theory of localization operators in other setting as the Laguerre Bessel setting. Following Wong's point of view,our main aim in this paper is to prove the analogues of the results on the localization operators studies by the authors in [1], [11], [12], [13], [14], [17] in the Laguerre-Bessel frame. The remainder of this paper is arranged as follows,in section 2 we recall the main results concerning the harmonic analysis associated with the Laguerre-Bessel transform and Schatten-Von Neumann classes,in section 3 we will study the boundedness,compactness and the Schatten properties of the two-Wavelet localization operator associated with the Laguerre-Bessel-Wigner transform.…”