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Related papers: Uncertainty principles for the Opdam-Cherednik tra…

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In this paper, we study the heat equation associated with the Jacobi--Cherednik operator on the real line. We establish some basic properties of the Jacobi--Cherednik heat kernel and heat semigroup. We also provide a solution to the Cauchy…

Functional Analysis · Mathematics 2025-01-14 Anirudha Poria , Ramakrishnan Radha

We prove unique continuation properties for solutions of evolution Schr\"odinger equation with time dependent potentials. In the case of the free solution these correspond to uncertainly principles referred to as being of Morgan type. As an…

Analysis of PDEs · Mathematics 2014-02-26 L. Escauriaza , C. E. Kenig , G. Ponce , L. Vega

Under Wigdersons' framework and by sorting out the technical points in the recent works of Tang (J. Fourier Anal. Appl. 31 (2025)) and Dias-Luef-Prata (J. Math. Pures Appl. (9) 198 (2025)), we prove an abstract uncertainty principle for…

Analysis of PDEs · Mathematics 2025-06-19 Tianxiao Huang , Ze Li , Jiani Liu

We prove the Shannon's inequality on non-collapsing $\mathsf{RCD}(0,N)$ spaces. In the proof, we use the characterization of the $\mathsf{EVI}_{0,N}$-gradient flow of the relative entropy and the infinitesimal behavior of the heat kernel.…

Metric Geometry · Mathematics 2024-11-08 Yu Kitabeppu

The aim of this paper is to prove new uncertainty principles for an integral operator $\tt$ with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of Faris's local uncertainty principle…

Classical Analysis and ODEs · Mathematics 2018-08-27 Saifallah Ghobber , Philippe Jaming

In this paper, we have investigated the thermodynamics of Schwarzschild black holes using the symmetric generalized uncertainty principle which contains correction terms involving momentum and position uncertainty. We obtain the…

General Relativity and Quantum Cosmology · Physics 2016-05-11 Abhijit Dutta , Sunandan Gangopadhyay

As a time-shifted and frequency-modulated version of the linear canonical transform (LCT), the offset linear canonical transform (OLCT) provides a more general framework of most existing linear integral transforms in signal processing and…

Signal Processing · Electrical Eng. & Systems 2019-01-30 Haiye Huo , Wenchang Sun , Li Xiao

Let $f$ be a finite signal. The classical uncertainty principle tells us that the product of the support of $f$ and the support of $\hat{f}$, the Fourier transform of $f$, must satisfy $|supp(f)|\cdot|supp(\hat{f})|\geq |G|$. Recently,…

Classical Analysis and ODEs · Mathematics 2025-09-08 A. Iosevich , I. Li , Z. Li , E. Yu

For the first time, the estimates of the non-centered Weyl-group invariant heat kernel for curved Riemannian spaces and for Opdam-Cherednik Laplacians are studied systematically. We prove sharp estimates for the root system $A_1$ with…

Representation Theory · Mathematics 2023-04-17 Piotr Graczyk , Patrice Sawyer

Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this…

Probability · Mathematics 2020-06-11 Jeremiah Birrell , Luc Rey-Bellet

The aim of this article is to formulate some novel uncertainty principles for the continuous shearlet transforms in arbitrary space dimensions. Firstly, we derive an analogue of the Pitt's inequality for the continuous shearlet transforms,…

Functional Analysis · Mathematics 2019-06-05 Firdous A. Shah , Azhar Y. Tantary

In this article, we study the Schr\"odinger equation posed in the Euclidean space. We prove observability inequalities for measurable sets that are thick with respect to decaying densities. The proof relies on quantitative uncertainty…

Analysis of PDEs · Mathematics 2026-02-23 Kévin Le Balc'h , Jiaqi Yu

In this article we prove both norm and modular Hardy inequalities for a class functions in one-dimensional fractional Orlicz-Sobolev spaces.

Analysis of PDEs · Mathematics 2020-09-15 Ariel Salort

In this article we consider linear operators satisfying a generalized commutation relation of a type of the Heisenberg-Lie algebra. It is proven that a generalized inequality of the Hardy's uncertainty principle lemma follows. Its…

Functional Analysis · Mathematics 2015-05-19 Toshimitsu Takaesu

We give a new proof of Hardy's uncertainty principle, up to the end-point case, which is only based on calculus. The method allows us to extend Hardy's uncertainty principle to Schr\"odinger equations with non-constant coefficients. We also…

Analysis of PDEs · Mathematics 2019-12-19 L. Escauriaza , C. E. Kenig , G. Ponce , L. Vega

Classical results due to Ingham and Paley-Wiener characterize the existence of nonzero functions supported on certain subsets of the real line in terms of the pointwise decay of the Fourier transforms. We view these results as uncertainty…

Functional Analysis · Mathematics 2016-06-01 Mithun Bhowmik , Swagato K. Ray , Suparna Sen

Some fundamental aspects related with the construction of Robertson-Schr\"odinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum…

Quantum Physics · Physics 2018-03-14 Orfeu Bertolami , Alex E. Bernardini , Pedro Leal

A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…

Quantum Physics · Physics 2015-06-16 G. M. Bosyk , T. M. Osán , P. W. Lamberti , M. Portesi

This paper studies the uncertainty principle for spherical $h$-harmonic expansions on the unit sphere of $\mathbb{R}^d$ associated with a weight function invariant under a general finite reflection group, which is in full analogy with the…

Classical Analysis and ODEs · Mathematics 2015-11-18 Han Feng

The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements,…

Quantum Physics · Physics 2011-03-02 Mario Berta , Matthias Christandl , Roger Colbeck , Joseph M. Renes , Renato Renner