Localization Operators and Uncertainty Principles for the Hankel Wavelet Transform

2021 ◽  
Vol 58 (3) ◽  
pp. 335-357
Author(s):  
Saifallah Ghobber ◽  
Siwar Hkimi ◽  
Slim Omri
Keyword(s):  
Wavelet Transform ◽  
Uncertainty Principles ◽  
Localization Operators ◽  
Localization Operator ◽  
Uncertainty Inequalities

The aim of this paper is to prove some uncertainty inequalities for the continuous Hankel wavelet transform, and study the localization operator associated to this transformation.

Localization operators, time frequency concentration and quantitative-type uncertainty for the continuous wavelet transform associated with spherical mean operator

2019 ◽  
Vol 17 (04) ◽  
pp. 1950022 ◽  
Author(s):  
Hatem Mejjaoli ◽  
Nadia Ben Hamadi ◽  
Slim Omri
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Finite Measure ◽  
Continuous Wavelet ◽  
Uncertainty Principles ◽  
Localization Operators ◽  
Spherical Mean Operator ◽  
Von Neumann ◽  
Time Frequency ◽  
Spherical Mean

We consider the continuous wavelet transform [Formula: see text] associated with the spherical mean operator. We investigate the localization operators for [Formula: see text], in particular, we prove that they are in the Schatten-von Neumann class. Next, we analyze the concentration of this transform on sets of finite measure. In particular, Donoho-Stark and Benedicks-type uncertainty principles are given. Finally, we prove many versions of quantitative uncertainty principles for [Formula: see text].

A variety of uncertainty principles for the Dunkl transform on ℝd

2020 ◽  
pp. 2150077
Author(s):  
Fethi Soltani
Keyword(s):  
Dunkl Transform ◽  
Uncertainty Principles ◽  
Local Type ◽  
Heisenberg Type ◽  
Uncertainty Inequalities

In this work, we prove Clarkson-type and Nash-type inequalities in the Dunkl setting on [Formula: see text] for [Formula: see text]-functions. By combining these inequalities, we show Heisenberg-type inequalities for the Dunkl transform on [Formula: see text], and we deduce local-type uncertainty inequalities for the Dunkl transform on [Formula: see text].

Weighted inequalities and uncertainty principles for the (k,a)-generalized Fourier transform

2016 ◽  
Vol 27 (03) ◽  
pp. 1650019 ◽  
Author(s):  
Troels Roussau Johansen
Keyword(s):  
Fourier Transform ◽  
Young Inequality ◽  
Uncertainty Principles ◽  
Weighted Inequalities ◽  
Generalized Fourier Transform ◽  
Pitt’S Inequality ◽  
Uncertainty Inequalities

We obtain several versions of the Hausdorff–Young and Hardy–Littlewood inequalities for the [Formula: see text]-generalized Fourier transform recently investigated at length by Ben Saïd, Kobayashi, and Ørsted. We also obtain a number of weighted inequalities — in particular Pitt’s inequality — that have application to uncertainty principles. Specifically we obtain several analogs of the Heisenberg–Pauli–Weyl principle for [Formula: see text]-functions, local Cowling–Price-type inequalities, Donoho–Stark-type inequalities and qualitative extensions. We finally use the Hausdorff–Young inequality as a means to obtain entropic uncertainty inequalities.

scholarly journals A Variation on Uncertainty Principle and Logarithmic Uncertainty Principle for Continuous Quaternion Wavelet Transforms

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino
Keyword(s):  
Wavelet Transform ◽  
Uncertainty Principle ◽  
Wavelet Transforms ◽  
Quaternion Algebra ◽  
Uncertainty Principles ◽  
Quaternion Fourier Transform ◽  
Coordinate Form ◽  
Quaternion Wavelet Transform ◽  
Polar Coordinate ◽  
Extended Uncertainty

The continuous quaternion wavelet transform (CQWT) is a generalization of the classical continuous wavelet transform within the context of quaternion algebra. First of all, we show that the directional quaternion Fourier transform (QFT) uncertainty principle can be obtained using the component-wise QFT uncertainty principle. Based on this method, the directional QFT uncertainty principle using representation of polar coordinate form is easily derived. We derive a variation on uncertainty principle related to the QFT. We state that the CQWT of a quaternion function can be written in terms of the QFT and obtain a variation on uncertainty principle related to the CQWT. Finally, we apply the extended uncertainty principles and properties of the CQWT to establish logarithmic uncertainty principles related to generalized transform.

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