Related papers: Uncertainty Principle for the Cantor Dyadic Group
We show that a well known uncertainty principle for functions on the circle can be derived from an uncertainty principle for the Euclidean motion group.
A directional time-frequency localization measure for functions defined on the $d$-dimensional Euclidean space is introduced. A connection between this measure and its periodic counterpart is established. For a class of functions, an…
We study a localization of functions defined on Vilenkin groups. To measure the localization we introduce two uncertainty products $UP_{\lambda}$ and $UP_{G}$ that are similar to the Heisenberg uncertainty product. $UP_{\lambda}$ and…
In this paper we introduce a notion of a directional uncertainty product for multivariate periodic functions. It measures a localization of a function along a particular direction. We study properties of the uncertainty product and give an…
In this paper the uncertainty principle is found via characteristics of continuous and nowhere differentiable functions. We prove that any physical system that has a continuous and nowhere differentiable position function is subject to an…
In this article, we establish several fundamental uncertainty principles for the Strichartz Fourier transform on the Heisenberg group, including Benedicks' theorem, the Donoho-Stark principle, the local uncertainty principle of Price, and a…
We approach uncertainty principles of Cowling-Price-Heis-\\enberg-type as a variational principle on modulation spaces. In our discussion we are naturally led to compact localization operators with symbols in modulation spaces. The optimal…
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…
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…
Motivated by results of Dyatlov on Fourier uncertainty principles for Cantor sets and by similar results of Knutsen for joint time-frequency representations (i.e., the short-time Fourier transform (STFT) with a Gaussian window, equivalent…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…
This paper focuses on the complex relationship between Heisenberg's Uncertainty Principle and the nodal structure of wave functions in a variety of quantum systems including the quantum harmonic oscillator, the particle in a 1D box , and…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks). We further give a new interpretation of the uncertainty principles as a statement about the time-frequency localization of elements of an…
We extend the classical Heisenberg uncertainty principle to a fractional $L^p$ setting by investigating a novel class of uncertainty inequalities derived from the fractional Schr\"odinger equation. In this work, we establish the existence…
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…
A universal formulation of uncertainty relations for quantum measurements is presented with additional focus on the representability of quantum observables by classical observables over a given state. Owing to the simplicity and operational…
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…
Classes of locally compact groups having qualitative uncertainty principle for Gabor transform have been investigated. These include Moore groups, Heisenberg Group $\mathbb{H}_n, \mathbb{H}_{n} \times D,$ where $D$ is discrete group and…