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Spectral theorems for Wigner transform associated with the Jacobi-Dunkl localization operators

Article scientifique 2023 Anglais

Résumé

Abstract The main purpose of this paper is to define the Wigner transform associated with the Jacobi-Dunkl operator and to give some results related to this transform as inversion formula, 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 Sp for all p ∈ [1; +∞] and we give a trace formula. MSC2020-Mathematics Subject Classification: 42B10, 47G30, 47B10.

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Chana, A., Akhlidj, A. (2023). Spectral theorems for Wigner transform associated with the Jacobi-Dunkl localization operators. https://doi.org/10.21203/rs.3.rs-2938438/v1

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Auteur(s)

Ahmed Chana Abdellatif Akhlidj

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