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;
D O I：
暂无
中图分类号：
学科分类号：
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.
引用
收藏
相关论文
共 101 条
[1]  
Abreu-Blaya Ricardo(2010)Extension Theorem for Complex Clifford Algebras-Valued Functions on Fractal Domains Boundary Value Problems 2010 513186-481
[2]  
Bory-Reyes Juan(2013)Beckner logarithmic uncertainty principle for the Riemann–Liouville operator Int. J. Math. 24 1350070-18
[3]  
Bosch Paul(2015)Uncertainty principle in terms of entropy for the Riemann–Liouville operator Bull. Malays. Math. Sci. Soc. 39 457-201
[4]  
Amri B(2006)The two-dimensional Clifford Fourier transform J. Math. Imaging 26 5-624
[5]  
Rachdi LT(2009)The Fourier transform in Clifford analysis Adv. Imaging Electron Phys. 156 55-38
[6]  
Amri B(2013)Convolution Products for Hypercomplex Fourier Transforms Journal of Mathematical Imaging and Vision 48 606-181
[7]  
Rachdi LT(2013)A general geometric fourier transform convolution theorem Adv. Appl. Clifford Algebra 23 15-153
[8]  
Brackx F(2008)The uncertainty principle associated with the continuous shearlet transform Int. J. Wavelets Multiresolut. Inf. Process. 6 157-624
[9]  
De Schepper N(2001)Clifford analysis: history and perspective Comput. Methods Funct. Theory 1 107-8
[10]  
Sommen F(1928)The Quantum Theory of the Electron Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 117 610-309
12345678910