Time-frequency analysis for the multidimensional Gabor Transform

被引：0

作者：

Ahmed Chana ^{[1
]}

Abdellatif Akhlidj ^{[1
]}

机构：

[1] 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

来源：

ANNALI DELL'UNIVERSITA' DI FERRARA | 2025年 / 71卷 / 1期

关键词：

35J05; 42A38; 42A63; 47B10; Gabor transform; Localization operators; Multidimensional Bessel operator; Time-frequency analysis; Uncertainty principles;

D O I：

10.1007/s11565-024-00558-w

中图分类号：

学科分类号：

摘要：

The main crux of this paper is to introduce a new integral transform called the multidimensional Hankel–Gabor transform and to give some new results related to this transform as Plancherel’s, Parseval’s, inversion and Calderón’s reproducing formulas. Next, we analyse the concentration of this transform on sets of finite measure and we give uncertainty principle for orthonormal sequences and Donoho–Stark’s type uncertainty principle. Last, we introduce a new class of pseudo-differential operator Lu,v(σ) called localization operator which 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 this operator belongs to the Schatten-Von Neumann classes Sp for all p∈[1;+∞] and we give a trace formula. © The Author(s) under exclusive license to Università degli Studi di Ferrara 2024.

引用

共 24 条

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