Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Asian-European Journal of Mathematics

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

Othman Tyr, Abdelaali Dades

Published Jun 16, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s1793557126500804

Related papers

An uncertainty principle for the basic wavelet transform

Javid Ahmad Ganie, Renu Jain

The aim of this paper is to derive the uncertainty principle which has implications in signal analysis and in quantum mechanics. First, we derive the definition of the wavelet transform in [Formula: see text]-calculus by using some weight function. Certain properties like linearity, scaling, translation, etc. were discussed. Later on, to illustrate this integral transform several results were derived for the effectiveness and performance of the proposed method. Also, this paper surveys recent applications to establish generalized uncertainty principle.

International Journal of Wavelets Multiresolution and Information Processing•Feb 24, 2021•4 citations

Heisenberg-Type Inequality and Localization Operators Associated to the Continuous Laguerre-Bessel Wavelet Transform

Abdelaali Dades, Radouan Daher

International Journal of Applied and Computational Mathematics•Sep 12, 2024•0 citations

Shapiro’s uncertainty principle and localization operators associated to the continuous wavelet transform

Nadia Ben Hamadi, H. Lamouchi

Journal of Pseudo-Differential Operators and Applications•Oct 3, 2016•14 citations

A generalization of Frenkel's formula

Shmuel Friedland

We generalize Frenkel's integral formula for traces of operators to operators. The resulting formula holds for bounded self-adjoint positive operators and $p$-Schatten class of compact positive operators.

math.FACross-listedarXiv:2602.10962•Feb 12, 2026

Wigner function and weyl transform, trace class

Mykola Yaremenko

The connection between cross-ambiguity and cross-Wigner functions is studied. The correspondence between the class of symbols and the Weyl operators is established; we obtain the necessary and sufficient conditions on the symbol under which the Weyl operator belongs to the trace class. The theory of Kaster-Loupias-Miracle is developed and the exact conditions on the Weyl operator to be positively defined in the Hilbert space is established.

Research in Mathematics•May 11, 2022•0 citations

Windowed fourier transform and general wavelet algorithms in quantum computation

MaGuangsheng, LiHongbo, ZhaoJiman

In this paper, we define the quantum windowed Fourier transform and study some of its properties, then we develop two useful operations called quantum convolution and 'integral'. Quantum 'integral'...

Quantum Information and Computation•Mar 1, 2019•1 citation
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.
The aim of this paper is to derive the uncertainty principle which has implications in signal analysis and in quantum mechanics. First, we derive the definition of the wavelet transform in [Formula: see text]-calculus by using some weight function. Certain properties like linearity, scaling, translation, etc. were discussed. Later on, to illustrate this integral transform several results were derived for the effectiveness and performance of the proposed method. Also, this paper surveys recent applications to establish generalized uncertainty principle.
We generalize Frenkel's integral formula for traces of operators to operators. The resulting formula holds for bounded self-adjoint positive operators and ppp-Schatten class of compact positive operators.