English
Related papers

Related papers: Uncertainty principle via variational calculus on …

200 papers

We present some forms of uncertainty principle which involve in a new way localization operators, the concept of $\varepsilon$-concentration and the standard deviation of $L^2$ functions. We show how our results improve the classical…

Functional Analysis · Mathematics 2015-10-12 Paolo Boggiatto , Evanthia Carypis , Alessandro Oliaro

We introduce a notion of localization for dyadic functions, i.e. functions defined on the Cantor group. Localization is characterized by functional $UC_d$ similar to the Heisenberg uncertainty constant used for real-line functions. We are…

Classical Analysis and ODEs · Mathematics 2013-12-10 Aleksander V. Krivoshein , Elena A. Lebedeva

The uncertainty principle constitutes one of the famous physical concepts which continues to attract researchers from different related fields since its discovery due to its utility in many applications. Among the classical (Fourier-based)…

Mathematical Physics · Physics 2024-04-04 Sabrine Arfaoui , Hicham Banouh , Anouar Ben Mabrouk

We establish uncertainty principles on compact Riemannian manifolds without boundary in the setting of Laplace-Beltrami operators, including the case of real-valued singular potentials. We replace the classical homogeneity assumption by a…

Classical Analysis and ODEs · Mathematics 2026-04-20 A. Iosevich , C. Park

We examine inverse problems for the variable-coefficient nonlocal parabolic operator $(\partial_t - \Delta_g)^s$, where $0 < s < 1$. This article makes two primary contributions. First, we introduce a novel entanglement principle for these…

Analysis of PDEs · Mathematics 2025-10-22 Ru-Yu Lai , Yi-Hsuan Lin , Lili Yan

In this note, we prove a new uncertainty principle for functions with radial symmetry by differentiating a radial version of the Stein-Weiss inequality. The difficulty is to prove the differentiability in the limit of the best constant…

Functional Analysis · Mathematics 2025-08-13 Jacopo Bellazzini , Matteo Nesi

We consider the inverse boundary value problem of determining a coefficient function in an elliptic partial differential equation from knowledge of the associated Neumann-Dirichlet-operator. The unknown coefficient function is assumed to be…

Analysis of PDEs · Mathematics 2023-05-17 Bastian Harrach

We study the Heisenberg-Pauli-Weyl uncertainty principle and the Caffarelli-Kohn-Nirenberg interpolation inequalities, on metric measure spaces satisfying measure contraction property. Using localization techniques, we show that these…

Metric Geometry · Mathematics 2023-09-06 Bang-Xian Han , Zhefeng Xu

The aim of this paper is establish the Heisenberg-Pauli-Weyl uncertainty principle and Donho-Stark's uncertainty principle for the Weinstein $L^2$-multiplier operators.

Classical Analysis and ODEs · Mathematics 2020-02-24 Ahmed Saoudi

Within the Heisenberg's uncertainty principle it is explicitly discussed the impact of these inequalities on the theory of integrated photonics at sub-wavelength regime. More especially, the uncertainty of the effective index values in…

Quantum Physics · Physics 2016-04-04 Bruno Bêche , E Gaviot

In this paper, an analogous of Heisenberg inequality is established for Laguerre-Bessel transform. Also, a local uncertainty principle for this transform is investigate

Classical Analysis and ODEs · Mathematics 2011-05-30 Soumeya Hamem , Lotfi Kamoun

We consider a linear ill-posed equation in the Hilbert space setting under white noise. Known convergence results for the discrepancy principle are either restricted to Hilbert-Schmidt operators (and they require a self-similarity condition…

Numerical Analysis · Mathematics 2021-04-14 Tim Jahn

We classify self-adjoint first-order differential operators on weighted Bergman spaces on the unit disc and answer questions related to uncertainty principles for such operators. Our main tools are the discrete series representations of…

Complex Variables · Mathematics 2022-06-22 Jens Gerlach Christensen , Christopher Benjamin Deng

The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore,…

Numerical Analysis · Mathematics 2025-07-01 Christian Offen

It is widely believed that combining the uncertainty principle with gravity will lead to an effective minimum length scale. A particular challenge is to specify this scale in a coordinate-independent manner so that covariance is not broken.…

High Energy Physics - Theory · Physics 2019-10-07 Jason Pye

The uncertainty principle is fundamentally rooted in the algebraic asymmetry between observables. We introduce a new class of uncertainty relations grounded in the resource theory of asymmetry, where incompatibility is quantified by an…

Quantum Physics · Physics 2026-02-10 Xingze Qiu

We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [1] and Zozor et al. [2]. Those inequalities can be considered as…

Probability · Mathematics 2009-04-14 Steeve Zozor , Mariela Portesi , Christophe Vignat

We prove two forms of uncertainty principle for the Schr\"odinger group generated by the Ornstein-Uhlenbeck operator. As a consequence, we derive a related (in fact, equivalent) result for the imaginary harmonic oscillator.

Analysis of PDEs · Mathematics 2024-06-25 Nicola Garofalo

In this article we consider a homogeneous eigenvalue problem ruled by the fractional $g-$Laplacian operator whose Euler-Lagrange equation is obtained by minimization of a quotient involving Luxemburg norms. We prove existence of an infinite…

Analysis of PDEs · Mathematics 2022-05-20 Julian Fernandez Bonder , Ariel Salort , Hernan Vivas

Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…

Quantum Physics · Physics 2026-05-27 Haruki Yamashita , Aina Mayumi , Gen Kimura