Mathematical Analysis and its Contemporary Applications

Spectral theorems associated with the generalized Dunkl-Wigner localization operators

10.30495/maca.2025.2051018.1122
Volume 7, Issue 2
Spring 2025
Pages 15-30
Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Authors

Ahmed Chana
Abdellatif Akhlidj

Laboratory of Fundamental and Applied Mathematics, Department of Mathematics and Informatics, Faculty of Sciences Ain Chock, University of Hassan II, B.P 5366 Maarif, Casablanca, Morocco

Abstract
The main crux of this paper is to introduce the Wigner transform associated with the generalized Dunkl operator and to give some new results related to this transform. Next, we introduce a new class of pseudo-differential operator $\mathcal{L}_{\psi_1, \psi_2}(\sigma)$ called localization operator which depends on a symbol $\sigma$ and two admissible functions $\psi_1$ and $\psi_2$, we give a criteria in terms of the symbol $\sigma$ for its boundedness and compactness, we also show that these operators belong to the Schatten-Von Neumann class $S^p$ for all $p \in [1, +\infty]$ and we give a trace formula.

Keywords

Fourier-Wigner transform
Localization operators
Dunkl operator
Schatten-von Neumann classes
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  • Receive Date 18 January 2025
  • Revise Date 08 February 2025
  • Accept Date 12 February 2025

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