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Ahmed Saoudi

Publications and source records attributed to Ahmed Saoudi.

8 recordsLinked to original sources
arXiv2026

Quadratic-Phase Fourier--Bessel Transform: definitions, properties and uncertainty principles

In this manuscript, we introduce the quadratic--phase Fourier--Bessel transform and develop its foundational properties, including continuity, the Riemann--Lebesgue lemma, reversibility, and Parseval's identity. We define the associated translation operator and convolution product, establishing their main properties within this framework. As an application, we prove a Donoho-Stark-type uncertainty principle for the quadratic-phase Fourier--Bessel transform, extending classical uncertainty results to this generalized setting.

math-ph↗
arXiv2025

Quadratic-Phase Dunkl Transform: Fundamental properties, translation operators, convolution product and HUP

In this paper, we introduce and study the quadratic-phase Dunkl transform, a novel integral transform on the real line parameterized by five real numbers $(a, b, c, d, e)$ and a multiplicity parameter $μ\geq -1/2$. We define the transform and establish its fundamental properties, including continuity, a Riemann--Lebesgue lemma, linearity, scaling, and most importantly, a reversibility theorem and an associated Parseval formula. We show that this novel quadratic-phase integral type transform generalizes a wide class of known transforms, such as the quadratic-phase Fourier-Bessel transform, the quadratic-phase Fourier transform, the linear canonical Dunkl transform, the fractional Dunkl transform, and the classical Dunkl transform, by choosing the appropriate specialization of its parameters. Furthermore, we introduce and investigate a corresponding quadratic-phase Dunkl translation operator and a convolution structure, proving their basic properties and a Young's inequality. Finally, we establish a new Heisenberg-type uncertainty principle for the quadratic-phase Dunkl transform, which extends the classical uncertainty principle for a large class of integral type transforms.

math.GM↗
arXiv2025

Continous linear canonical Dunkl wavelet transform: properties and applications

The aim of this paper is to establish and study the linear canonical Dunkl wavelet transform. We begin by introducing the generalized translation operator and generalized convolution product for the linear canonical Dunkl transform and we establish their basic properties. Next, we introduce the new proposed wavelet transform and we investigate its fundamentals properties. In the end, we derive some uncertainty inequalities for the desired wavelet transform as applications.

math.CA↗
arXiv2020

Time-frequency Analysis of two-wavelet theory in Weinstein setting

In this paper, we introduce the notion of Weinstein two-wavelet and we define the two-wavelet localization operators in the setting of the Weinstein theory. Then we give a host of sufficient conditions for the boundedness and compactness of the two-wavelet localization operator on $L^{p}_α(\mathbb{R}^{d+1}_+)$ for all $1\leq p\leq \infty$, in terms of properties of the symbol $σ$ and the functions $φ$ and $ψ$. In the end, we study some typical examples of the Weinstein two-wavelet localization operators.

math.AP↗
arXiv2020

Two-wavelet theory in Weinstein setting

In this paper we introduce the notion of a Weinstein two-wavelet. Then we establish and prove the resolution of the identity formula for the Weinstein continuous wavelet transform. Next, we give results on Calderón's type reproducing formula in the context of the Weinstein two-wavelet.

math.AP↗
arXiv2018

A variation of the $L^p$ uncertainty principles for the Weinstein transform

The Weinstein operator has several applications in pure and applied Mathematics especially in Fluid Mechanics and satisfies some uncertainty principles similar to the Euclidean Fourier transform. The aim of this paper is establish a generalization of uncertainty principles for Weinstein transform in $L_α^p$-norm. Firstly, we extend the Heisenberg-Pauli-Weyl uncertainty principle to more general case. Then we establish three continuous uncertainty principles of concentration type. The first and the second uncertainty principles are $L_α^p$ versions and depend on the sets of concentration $Ω$ and $Σ$, and on the time function $φ$. However, the third uncertainty principle is also $L_α^p$ version depends on the sets of concentration and he is independent on the band limited function $φ$. These $L_α^p$-Donoho-Stark-type inequalities generalize the results obtained in the case $p=q=2$.

math.AP↗