A Local Uncertainty Principle

1984 ◽  
Vol 15 (5) ◽  
pp. 988-995
Author(s):  
John J. Benedetto
Keyword(s):  
Uncertainty Principle ◽  
Local Uncertainty Principle ◽  
Local Uncertainty

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.

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 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 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.

The Uncertainty Principle Derived by The Finite Transmission Speed of Light and Information

2014 ◽  
Vol 3 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Piero Chiarelli
Keyword(s):  
Uncertainty Principle ◽  
Large Scale ◽  
Uncertainty Relations ◽  
Speed Of Light ◽  
Energy Fluctuation ◽  
Hydrodynamic Analogy ◽  
Non Local ◽  
Minimum Uncertainty ◽  
Quantum Hydrodynamic ◽  
Transmission Speed

This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle is fully compatible with the postulate of finite transmission speed of light and information. The theory shows that the measurement process performed in the large scale classical limit in presence of background noise, cannot have a duration smaller than the time need to the light to travel the distance up to which the quantum non-local interaction extend itself. The product of the minimum measuring time multiplied by the variance of energy fluctuation due to presence of stochastic noise shows to lead to the minimum uncertainty principle. The paper also shows that the uncertainty relations can be also derived if applied to the indetermination of position and momentum of a particle of mass m in a quantum fluctuating environment.

The inner bound of quantum spacetime

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Wigner Function ◽  
Uncertainty Principle ◽  
Quantum Spacetime

This article addresses the connection of the UNCERTAINTY PRINCIPLE with the WIGNER FUNCTION.

The uncertainty principle between the Hubble parameter and the volume of space.

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Uncertainty Principle ◽  
Hubble Parameter

The uncertainty principle between the Hubble parameter and the volume of space.

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