Clifford Wavelet Transform and the Uncertainty Principle

被引:0
作者
Hicham Banouh
Anouar Ben Mabrouk
Mhamed Kesri
机构
[1] Université de Sciences et Technologie Houari Boumedienne,Laboratoire de Systèmes Dynamiques et Géométrie, Faculté de Mathématiques
[2] University of Kairaouan,Higher institut of Applied Mathematics and Computer Sciences
[3] Laboratory of Algebra,Department of Mathematics, Faculty of Sciences
[4] Number Theory and Nonlinear Analysis LR18ES15,Department of Mathematics, Faculty of Sciences
[5] University of Tabuk,Département d’analyse, Faculté de Mathématiques
[6] Université de Sciences et Technologie Houari Boumedienne,undefined
来源
Advances in Applied Clifford Algebras | 2019年 / 29卷
关键词
Harmonic analysis; Clifford algebra; Clifford analysis; Continuous wavelet transform; Clifford Fourier transform; Clifford wavelet transform; Uncertainty principle; 30G35; 42C40; 42B10; 15A66;
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摘要
The present paper lies in the whole topic of wavelet harmonic analysis on Clifford algebras. In which we derive a Heisenberg-type uncertainty principle for the continuous Clifford wavelet transform. A brief review of Clifford algebra/analysis, wavelet transform on R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}$$\end{document} and Clifford Fourier transform and their properties is conducted. Next, such concepts are applied to develop an uncertainty principle based on Clifford wavelets.
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