scholarly journals Uncertainty Principles for the Dunkl-Wigner Transforms

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Fethi Soltani
Keyword(s):  
Uncertainty Principle ◽  
Uncertainty Principles ◽  
Wigner Transform ◽  
Heisenberg Type ◽  
Local Uncertainty Principle ◽  
Local Uncertainty

We prove a version of Heisenberg-type uncertainty principle for the Dunkl-Wigner transform of magnitude s>0; and we deduce a local uncertainty principle for this transform.

scholarly journals Helgason–Gabor–Fourier transform and uncertainty principles

2020 ◽  
pp. 2050056
Author(s):  
Mustapha Boujeddaine ◽  
Mohammed El Kassimi ◽  
Saïd Fahlaoui
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principle ◽  
Plancherel Formula ◽  
Riemannian Symmetric Space ◽  
Uncertainty Principles ◽  
Reconstruction Formula ◽  
Time Frequency ◽  
Local Uncertainty Principle ◽  
Local Uncertainty ◽  
Parseval Formula

Windowing a Fourier transform is a useful tool, which gives us the similarity between the signal and time frequency signal, and it allows to get sense when/where certain frequencies occur in the input signal, this method was introduced by Dennis Gabor. In this paper, we generalize the classical Gabor–Fourier transform (GFT) to the Riemannian symmetric space calling it the Helgason–Gabor–Fourier transform (HGFT). We prove several important properties of HGFT like the reconstruction formula, the Plancherel formula and Parseval formula. Finally, we establish some local uncertainty principle such as Benedicks-type uncertainty principle.

scholarly journals A variety of uncertainty principles for the Hankel-Stockwell transform

2021 ◽  
Vol 5 (1) ◽  
pp. 22-34
Author(s):  
Khaled Hleili ◽  
◽  
Keyword(s):  
Uncertainty Principle ◽  
Uncertainty Principles ◽  
Local Uncertainty Principle ◽  
Local Uncertainty ◽  
Pitt’S Inequality ◽  
Stockwell Transform

In this work, we establish \(L^p\) local uncertainty principle for the Hankel-Stockwell transform and we deduce \(L^p\) version of Heisenberg-Pauli-Weyl uncertainty principle. Next, By combining these principles and the techniques of Donoho-Stark we present uncertainty principles of concentration type in the \(L^p\) theory, when \(1< p\leqslant2\). Finally, Pitt's inequality and Beckner's uncertainty principle are proved for this transform.

Certifying Einstein-Podolsky-Rosen steering via the local uncertainty principle

2016 ◽  
Vol 93 (1) ◽  
Author(s):  
Yi-Zheng Zhen ◽  
Yu-Lin Zheng ◽  
Wen-Fei Cao ◽  
Li Li ◽  
Zeng-Bing Chen ◽  
...  
Keyword(s):  
Uncertainty Principle ◽  
Local Uncertainty Principle ◽  
Local Uncertainty ◽  
Einstein Podolsky Rosen

scholarly journals AN UNCERTAINTY PRINCIPLE FOR SOLUTIONS OF THE SCHRÖDINGER EQUATION ON -TYPE GROUPS

2020 ◽  
pp. 1-16
Author(s):  
AINGERU FERNÁNDEZ-BERTOLIN ◽  
PHILIPPE JAMING ◽  
SALVADOR PÉREZ-ESTEVA
Keyword(s):  
Schrödinger Equation ◽  
Uncertainty Principle ◽  
Schrodinger Equation ◽  
Schrodinger Equations ◽  
Nilpotent Lie Groups ◽  
Schrödinger Equations ◽  
Uncertainty Principles ◽  
Uniqueness Of Solutions ◽  
Free Case ◽  
Formula Type

In this paper we consider uncertainty principles for solutions of certain partial differential equations on $H$ -type groups. We first prove that, on $H$ -type groups, the heat kernel is an average of Gaussians in the central variable, so that it does not satisfy a certain reformulation of Hardy’s uncertainty principle. We then prove the analogue of Hardy’s uncertainty principle for solutions of the Schrödinger equation with potential on $H$ -type groups. This extends the free case considered by Ben Saïd et al. [‘Uniqueness of solutions to Schrödinger equations on H-type groups’, J. Aust. Math. Soc. (3)95 (2013), 297–314] and by Ludwig and Müller [‘Uniqueness of solutions to Schrödinger equations on 2-step nilpotent Lie groups’, Proc. Amer. Math. Soc.142 (2014), 2101–2118].

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].

scholarly journals The generalized and extended uncertainty principles and their implications on the Jeans mass

2019 ◽  
Vol 488 (1) ◽  
pp. L69-L74 ◽  
Author(s):  
H Moradpour ◽  
A H Ziaie ◽  
S Ghaffari ◽  
F Feleppa
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Ideal Gas ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Newtonian Gravity ◽  
Uncertainty Principles ◽  
Temperature Relation ◽  
Heisenberg Uncertainty Principle ◽  
Extended Uncertainty

ABSTRACT The generalized and extended uncertainty principles affect the Newtonian gravity and also the geometry of the thermodynamic phase space. Under the influence of the latter, the energy–temperature relation of ideal gas may change. Moreover, it seems that the Newtonian gravity is modified in the framework of the Rényi entropy formalism motivated by both the long-range nature of gravity and the extended uncertainty principle. Here, the consequences of employing the generalized and extended uncertainty principles, instead of the Heisenberg uncertainty principle, on the Jeans mass are studied. The results of working in the Rényi entropy formalism are also addressed. It is shown that unlike the extended uncertainty principle and the Rényi entropy formalism that lead to the same increase in the Jeans mass, the generalized uncertainty principle can decrease it. The latter means that a cloud with mass smaller than the standard Jeans mass, obtained in the framework of the Newtonian gravity, may also undergo the gravitational collapse process.

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