A sharp Clifford wavelet Heisenberg-type uncertainty principle

Hicham Banouh, Anouar Ben Mabrouk

Type: Article

Publication Date: 2020-09-01

Citations: 7

DOI: https://doi.org/10.1063/5.0015989

Abstract

In the present work, we are concerned with the development of a new uncertainty principle based on the wavelet transform in the Clifford analysis/algebra framework. We precisely derive a sharp Heisenberg-type uncertainty principle for the continuous Clifford wavelet transform.

Locations

Journal of Mathematical Physics - View
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	A sharp Clifford-wavelet Heisenberg-type uncertainty principle	2020	Hicham Banouh Anouar Ben Mabrouk
+	A sharp Clifford-wavelet Heisenberg-type uncertainty principle	2020	Hicham Banouh Anouar Ben Mabrouk
+ PDF Chat	Clifford Wavelet Transform and the Uncertainty Principle	2019	Hicham Banouh Anouar Ben Mabrouk Mhamed Kesri
+	Clifford-wavelet Transform and the uncertainty principle	2019	Hicham Banouh Anouar Ben Mabrouk Mohamed Kesri
+	Clifford-wavelet Transform and the uncertainty principle	2019	Hicham Banouh Anouar Ben Mabrouk Mohamed Kesri
+	Clifford wavelet transform and the associated Donoho-Stark's uncertainty Principle	2022	Sabrine Arfaoui
+	Heisenberg-type uncertainty inequalities for the Dunkl wavelet transform	2022	Saifallah Ghobber
+ PDF Chat	Logarithmic uncertainty principle for Clifford-wavelet transform	2024	Sabrine Arfaoui Hicham Banouh Anouar Ben Mabrouk
+ PDF Chat	Heisenberg Type Inequality for the Continuous Laguerre Wavelet Transform	2024	Abdelaali Dades Radouan Daher
+	Uncertainty inequalities for the continuous wavelet transform	1999	P. Singer
+	Uncertainty principles and integral equations associated with a quadratic‐phase wavelet transform	2023	L. P. Castro R. C. Guerra
+ PDF Chat	Correction to: Clifford Wavelet Transform and the Uncertainty Principle	2020	Hicham Banouh Anouar Ben Mabrouk Mhamed Kesri
+	Logarithmic uncertainty principles for the Hankel wavelet transform	2020	Saifallah Ghobber
+	Logarithmic uncertainty principles for the Hankel wavelet transform	2020	Saifallah Ghobber
+	Uncertainty principles for the continuous Hankel Wavelet transform	2016	C. Baccar
+ PDF Chat	A Quantum Wavelet Uncertainty Principle	2021	Sabrine Arfaoui Maryam G. Alshehri Anouar Ben Mabrouk
+	Clifford‐valued linear canonical wavelet transform and the corresponding uncertainty principles	2024	Shahbaz Rafiq M. Younus Bhat
+	Tighter Heisenberg–Weyl type uncertainty principle associated with quaternion wavelet transform	2023	Xinyu Wang Shenzhou Zheng
+	An uncertainty principle for the basic wavelet transform	2021	Javid Ahmad Ganie Renu Jain
+	Quantitative uncertainty principles associated with the k$$ k $$‐Hankel wavelet transform on ℝd$$ {\mathbb{R}}&#x0005E;d $$	2022	Hatem Mejjaoli Firdous A. Shah

Works That Cite This (6)

Action	Title	Year	Authors
+	Uncertainty principles of hypercomplex functions for fractional Fourier transform	2023	Wen‐Biao Gao
+ PDF Chat	Novel special affine wavelet transform and associated uncertainty principles	2020	Owais Ahmad Neyaz A. Sheikh
+ PDF Chat	Fractional Fourier Transform: Main Properties and Inequalities	2023	Mawardi Bahri Samsul Ariffin Abdul Karim
+	Uncertainty principles associated with multi-dimensional linear canonical transform	2021	Owais Ahmad A. Achak Neyaz A. Sheikh Ujwal Warbhe
+ PDF Chat	A Quantum Wavelet Uncertainty Principle	2021	Sabrine Arfaoui Maryam G. Alshehri Anouar Ben Mabrouk
+	Tighter Uncertainty Principles Associated with the Non-isotropic Angular Stockwell Transform	2024	Xinyu Wang Shenzhou Zheng

Works Cited by This (43)

Action	Title	Year	Authors
+ PDF Chat	Quaternion and Clifford Fourier Transforms and Wavelets	2013	Eckhard Hitzer Stephen J. Sangwine
+	Gabor Wavelets and the Heisenberg Group: Gabor Expansions and Short Time Fourier Transform from the Group Theoretical Point of View	1992	Hans G. Feichtinger Karlheinz Gröchenig
+ PDF Chat	Introductory Clifford Analysis	2015	Frank Sommen Hennie De Schepper
+	Chapter 2 The Fourier Transform in Clifford Analysis	2009	Fred Brackx Nele De Schepper Frank Sommen
+ PDF Chat	A General Geometric Fourier Transform	2013	Roxana Bujack Gerik Scheuermann Eckhard Hitzer
+	Stronger uncertainty principles for hypercomplex signals	2015	Yan Yang Pei Dang Tao Qian
+	Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl3,0	2006	Mawardi Bahri Eckhard Hitzer
+	CLIFFORD ALGEBRA Cl<sub>3,0</sub>-VALUED WAVELET TRANSFORMATION, CLIFFORD WAVELET UNCERTAINTY INEQUALITY AND CLIFFORD GABOR WAVELETS	2007	Mawardi Bahri Eckhard Hitzer
+	Clifford Fourier Transform on Multivector Fields and Uncertainty Principles for Dimensions n = 2 (mod 4) and n = 3 (mod 4)	2008	Eckhard Hitzer Mawardi Bahri
+	Uncertainty Principle in Terms of Entropy for the Riemann–Liouville Operator	2015	Besma Amri Lakhdar T. Rachdi