Related papers: Uncertainty principles for the windowed Hankel tra…
We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of…
We give a new proof of the $L^2$ version of Hardy's uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of optimal Gaussian decay…
By the important applications of Gabor transform in time-frequency analysis and signal analysis, in this paper, we consider the Gabor quaternion Fourier transform (GQFT), and we prove of it a version Benedicks-type uncertainty principle for…
Considering the existence of nonconformal stochastic fluctuations in the metric tensor a generalized uncertainty principle and a deformed dispersion relation (associated to the propagation of photons) are deduced. Matching our model with…
The two-sided quaternion Fourier transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization of Beurling's theorem, Hardy, Cowling-Price and Gelfand-Shilov theorems, is obtained for the…
We study a variant of the uncertainty principle in terms of the annihilation and creation operator on generalized Segal Bargmann spaces, which are used for the FBI-Bargmann transform. In addition, we compute the Berezin transform of these…
We prove the transfer principle for fractional Ornstein-Uhlenbeck processes, i.e., we construct a Brownian motion that has the same filtration as the fractional Ornstein-Uhlenbeck process and then represent the fractional Ornstein-Uhlenbeck…
Some aspects of application of the Uncertainty Principle in the range of interaction radiation with matter surveyed. The procedure of adjustment is proposed at calculation of values of an electromagnetic energy in a quantum theory of a…
In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The…
Motivated by the Generalized Uncertainty Principle, covariance, and a minimum measurable time, we propose a deformation of the Heisenberg algebra and show that this leads to corrections to all quantum mechanical systems. We also demonstrate…
Given a frame in C^n which satisfies a form of the uncertainty principle (as introduced by Candes and Tao), it is shown how to quickly convert the frame representation of every vector into a more robust Kashin's representation whose…
We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal…
From positions, attained by modern theoretical physics in understanding of the universe bases, the methodological and philosophical analysis of fundamental physical concepts and their formal and informal connections with the real economic…
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
The classical uncertainty principle of harmonic analysis states that a nontrivial function and its Fourier transform cannot both be sharply localized. It plays an important role in signal processing and physics. This paper generalizes the…
This comprehensive review paper delves into the intricacies of advanced Fourier type integral transforms and their mathematical properties, with a particular focus on fractional Fourier transform (FrFT), linear canonical transform (LCT),…
We establish anisotropic uncertainty principles (UPs) for general metaplectic operators acting on $L^2(\mathbb{R}^d)$, including degenerate cases associated with symplectic matrices whose $B$-block has nontrivial kernel. In this setting,…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
When propagating uncertainty in the data of differential equations, the probability laws describing the uncertainty are typically themselves subject to uncertainty. We present a sensitivity analysis of uncertainty propagation for…
For a simple set of observables we can express, in terms of transition probabilities alone, the Heisenberg Uncertainty Relations, so that they are proven to be not only necessary, but sufficient too, in order for the given observables to…