Advances in Pure Mathematics

Weinstein Gabor Transform and Applications

Hatem Mejjaoli, Ahmedou Ould Ahmed Salem

Published Jan 1, 2012• 21 citations

Abstract

In this paper we consider Weinstein operator. We define and study the continuous Gabor transform associated with this operator. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for it. As applications, we obtain analogous of Heisenberg’s inequality for the generalized continuous Gabor transform. At the end we give the practical real inversion formula for the generalized continuous Gabor transform.

DOI: 10.4236/apm.2012.23029

Related papers

Gabor transform in the generalized Weinstein theory setting

Mohamed Ben

In this paper, we consider the generalized Weinstein operator ?d,?,n W, we introduce and study the continuous generalized Weinstein Gabor Transform denoted by Gg associated with the operator ?d,?,n W. We prove a Plancherel formula and a weak uncertainty principle for it. We obtain analogous of Heisenbeg?s inequality for the generalized Weinstein Gabor Transform.

FilomatJan 1, 20240 citations

Uncertainty Principle for the Weinstein-Gabor Transforms

Imen Ali Kallel, A. Saoudi

In this paper, we present the localization of the ν-entropy for the Weinstein Gabor transform. Through the utilization of the ν-entropy, we establish an alternative expression for the Heisenberg uncertainty principle for the Weinstein Gabor transform. In addition, we further extend our study by elaborating on an Lp version of the Heisenberg uncertainty principle for the Weinstein Gabor transform.

International Journal of Analysis and ApplicationsMay 31, 20241 citation

Heisenberg Type Inequality for the Continuous Laguerre Wavelet Transform

Abdelaali Dades, Radouan Daher

Abstract In this work, some uncertainty inequalities associated to the Laguerre wavelet transform are established. Namely, Donoho-Stark and Heisenberg-Weyl type uncertainty principles are proved.

Mar 19, 20241 citation

Continuous stockwell transform and the uncertainty principle in relation to the poly-axially operator

Khaled Hleili, Manel Hleili

In this paper, we define and study the continuous Stockwell transform associated with the poly-axially operator. Next, we prove some new uncertainty principles for this transform. They include Heisenberg-type uncertainty principle and the Beckners uncertainty principle in term of entropy for Stockwell transform.

Asian-European Journal of MathematicsMar 7, 20251 citation

Uncertainty principles for the continuous wavelet transform associated with a Bessel type operator on the half line

Cyrine Baccar, Aicha Kabache

This paper presents uncertainty principles pertaining to generalized wavelet transforms associated with a second-order differential operator on the half line, extending the concept of the Bessel operator. Specifically, we derive a Heisenberg-Pauli-Weyl type uncertainty principle, as well as other uncertainty relations involving sets of finite measure

Malaya Journal of MatematikJul 1, 20241 citation

On the q-Weinstein wavelet transform and its associated localization operators

Othman Tyr, Abdelaali Dades

In this paper, we introduce the [Formula: see text]-Weinstein transform and investigate the associated translation operator and convolution product, highlighting some of their fundamental properties. We then develop the [Formula: see text]-Weinstein wavelet transform and examine the corresponding localization operators. In particular, we establish their trace class properties and prove that they belong to the Schatten–von Neumann class.

Asian-European Journal of MathematicsJun 16, 20260 citations