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Hardy's uncertainty principle is a classical result in harmonic analysis, stating that a function in $L^2(\mathbb{R}^d)$ and its Fourier transform cannot both decay arbitrarily fast at infinity. In this paper, we extend this principle to…

Analysis of PDEs · Mathematics 2025-04-03 Elena Cordero , Gianluca Giacchi , Eugenia Malinnikova

In this paper we propose a novel transform called continuous quaternionic stockwell transform. We express the admissibility condition in term of the (two-sided) quaternion Fourier transform . We show that its fundamental properties, such as…

Classical Analysis and ODEs · Mathematics 2019-12-25 Brahim Kamel , Emna Tefjeni

We present a novel generalization of the Heisenberg uncertainty principle which introduces the existence of a maximal observable momentum and at the same time does not entail a minimal indeterminacy in position. The above result is an exact…

High Energy Physics - Theory · Physics 2021-07-07 Luciano Petruzziello

Analytic number theorists usually seek to show that sequences which appear naturally in arithmetic are ``well-distributed'' in some appropriate sense. In various discrepancy problems, combinatorics researchers have analyzed limitations to…

Number Theory · Mathematics 2007-05-23 Andrew Granville , K. Soundararajan

The uncertainty principle is often interpreted by the tradeoff between the error of a measurement and the consequential disturbance to the followed ones, which originated long ago from Heisenberg himself but now falls into reexamination and…

Quantum Physics · Physics 2018-03-29 Yu-Xiang Zhang , Shengjun Wu , Zeng-Bing Chen

The classical uncertainty principles deal with functions on abelian groups. In this paper, we discuss the uncertainty principles for finite index subfactors which include the cases for finite groups and finite dimensional Kac algebras. We…

Operator Algebras · Mathematics 2015-11-12 Chunlan Jiang , Zhengwei Liu , Jinsong Wu

A central problem in signal processing and communications is to design signals that are compact both in time and frequency. Heisenberg's uncertainty principle states that a given function cannot be arbitrarily compact both in time and…

Information Theory · Computer Science 2014-01-17 Reza Parhizkar , Yann Barbotin , Martin Vetterli

The goal of this paper is to review the main trends in the domain of uncertainty principles and localization, emphasize their mutual connections and investigate practical consequences. The discussion is strongly oriented towards, and…

Information Theory · Computer Science 2013-09-23 Benjamin Ricaud , Bruno Torresani

We first present a generalization of the Robertson-Heisenberg uncertainty principle. This generalization applies to mixed states and contains a covariance term. For faithful states, we characterize when the uncertainty inequality is an…

Quantum Physics · Physics 2023-06-08 Stanley Gudder

In this paper, we study forms of the uncertainty principle suggested by problems in control theory. We obtain a version of the classical Paneah-Logvinenko-Sereda theorem for the annulus. More precisely, we show that a function with spectrum…

Classical Analysis and ODEs · Mathematics 2021-11-23 Walton Green , Benjamin Jaye , Mishko Mitkovski

We derive the uncertainty principle for a Dirac fermion in a torsion field obeying the Hehl-Datta (HD) equation. We first discuss that there should be a correction factor to the Heisenberg uncertainty principle (HUP) when torsional effects…

General Relativity and Quantum Cosmology · Physics 2020-06-17 Anjali Ramesh

In this work, we summarize the linearization method to study the Heisenberg Uncertainty Principles, and explain that the same approach can be used to handle the stability problem. As examples of application, combining with spherical…

Analysis of PDEs · Mathematics 2025-10-02 Xia Huang , Dong Ye

As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…

Quantum Physics · Physics 2019-09-18 Jie Xie , Songtao Huang , Li Zhou , Aonan Zhang , Huichao Xu , Man-Hong Yung , Nengkun Yu , Lijian Zhang

We generalize, improve and unify theorems of Rumin, and Maassen--Uffink about classical entropies associated to quantum density matrices. These theorems refer to the classical entropies of the diagonals of a density matrix in two different…

Mathematical Physics · Physics 2015-05-30 Rupert L. Frank , Elliott H. Lieb

We consider the Heisenberg uncertainty principle of position and momentum in 3-dimensional spaces of constant curvature $K$. The uncertainty of position is defined coordinate independent by the geodesic radius of spherical domains in which…

Quantum Physics · Physics 2018-06-01 Thomas Schürmann

The phenomenon in the essence of classical uncertainty principles is well known since the thirties of the last century. We introduce a new phenomenon which is in the essence of a new notion that we introduce: "Generalized Uncertainty…

Mathematical Physics · Physics 2008-07-15 Ronny Machluf

We prove sharp Pitt's inequality for the Dunkl transform in $L^{2}(\mathbb{R}^{d})$ with the corresponding weights. As an application, we obtain the logarithmic uncertainty principle for the Dunkl transform.

Classical Analysis and ODEs · Mathematics 2015-05-13 Dmitry Gorbachev , Valery Ivanov , Sergey Tikhonov

This note shows that Heisenberg's choice for a wave function in his original paper on the uncertainty principle is simply a renormalized characteristic function of a stable distribution with certain restrictions on the parameters. Relaxing…

Quantum Physics · Physics 2007-05-23 J. Orlin Grabbe

The emergence of the generalized uncertainty principle and the existence of a non-zero minimal length are intertwined. On the other hand, the Heisenberg uncertainty principle forms the core of the EPR paradox. Subsequently, here, the…

Quantum Physics · Physics 2022-02-16 S. Aghababaei , H. Moradpour

In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…

General Physics · Physics 2007-07-12 Elias P. Gyftopoulos