Time-frequency analysis associated with the Hartley-Wigner localization operators

Chana, Ahmed; Akhlidj, Abdellatif

doi:10.30495/maca.2025.2046585.1115

Time-frequency analysis associated with the Hartley-Wigner localization operators

10.30495/maca.2025.2046585.1115

Volume 7, Issue 1
Winter 2025

Pages 1-16

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 a new integral transform called the Hartley-Wigner transform 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 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

Hartley-Bessel operator

Schatten-von Neumann classes

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