Spectrum of the finite Dunkl transform operator and Donoho–Stark uncertainty principle

2012 ◽  
Vol 3 (2) ◽  
Author(s):  
Hichem Ben Aouicha ◽  
Chirine Chettaoui
Keyword(s):  
Uncertainty Principle ◽  
Dunkl Transform

SHAPIRO’S UNCERTAINTY PRINCIPLE IN THE DUNKL SETTING

2015 ◽  
Vol 92 (1) ◽  
pp. 98-110 ◽  
Author(s):  
SAIFALLAH GHOBBER
Keyword(s):  
Uncertainty Principle ◽  
Orthonormal Basis ◽  
Integral Transform ◽  
Reflection Group ◽  
Dunkl Transform ◽  
Time Frequency ◽  
Orthonormal Bases ◽  
Orthonormal Sequence ◽  
Finite Reflection Group ◽  
Uniformly Bounded

The Dunkl transform ${\mathcal{F}}_{k}$ is a generalisation of the usual Fourier transform to an integral transform invariant under a finite reflection group. The goal of this paper is to prove a strong uncertainty principle for orthonormal bases in the Dunkl setting which states that the product of generalised dispersions cannot be bounded for an orthonormal basis. Moreover, we obtain a quantitative version of Shapiro’s uncertainty principle on the time–frequency concentration of orthonormal sequences and show, in particular, that if the elements of an orthonormal sequence and their Dunkl transforms have uniformly bounded dispersions then the sequence is finite.

scholarly journals Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in L2

2016 ◽  
Vol 202 ◽  
pp. 109-118 ◽  
Author(s):  
D.V. Gorbachev ◽  
V.I. Ivanov ◽  
S.Yu. Tikhonov
Keyword(s):  
Uncertainty Principle ◽  
Dunkl Transform

Some shaper uncertainty principles for multivector-valued functions

2016 ◽  
Vol 14 (06) ◽  
pp. 1650043
Author(s):  
Minggang Fei ◽  
Yubin Pan ◽  
Yuan Xu
Keyword(s):  
Fourier Transform ◽  
Clifford Algebra ◽  
Uncertainty Principle ◽  
Dunkl Transform ◽  
Uncertainty Principles ◽  
Heisenberg Uncertainty Principle ◽  
Clifford Fourier Transform ◽  
Heisenberg Uncertainty ◽  
The Fourier Transform ◽  
Adjoint Operators

The Heisenberg uncertainty principle and the uncertainty principle for self-adjoint operators have been known and applied for decades. In this paper, in the framework of Clifford algebra, we establish a stronger Heisenberg–Pauli–Wely type uncertainty principle for the Fourier transform of multivector-valued functions, which generalizes the recent results about uncertainty principles of Clifford–Fourier transform. At the end, we consider another stronger uncertainty principle for the Dunkl transform of multivector-valued functions.

scholarly journals An uncertainty principle for the Dunkl transform

1999 ◽  
Vol 59 (3) ◽  
pp. 353-360 ◽  
Author(s):  
Margit Rösler
Keyword(s):  
Uncertainty Principle ◽  
Hermite Functions ◽  
Dunkl Transform

This note presents an analogue of the classical Heisenberg-Weyl uncertainty principle for the Dunkl transform on ℝN. Its proof is based on expansions with respect to generalised Hermite functions.

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.

Sign in / Sign up

Export Citation Format

Share Document