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

Abstract The main crux of this work is to study the Wigner transform associated with the Laguerre-Bessel operator and to give some results related to this transform. Next motivated by Wong's point of view we define a class of pseudo-differential operator Lu,v (σ) called localization operator wich depend on a symbol σ and two functions u and v, we give a criteria in terms of the symbol σ for its boundedness and compactness, we also show that these operators belongs to the Schatten-Von Neumann class S p for all p ∈ [1; + ∞] and we give a trace formula. MSC2020-Mathematics Subject Classification: 42B10, 47G30, 47B10.