Related papers: The Uncertainty Principle in Harmonic Analysis -- …
The uncertainty principle is one of the fundamental tools for time-frequency analysis in signal processing, revealing the intrinsic trade-off between time and frequency resolutions. With the continuous development of various advanced…
Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg Uncertainty Principle into the Generalized Uncertainty Principle. In this…
The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary…
The quantification of the "measurement uncertainty" aspect of Heisenberg's Uncertainty Principle---that is, the study of trade-offs between accuracy and disturbance, or between accuracies in an approximate joint measurement on two…
A Hamiltonian formalism is used to describe ensembles of fields in terms of two canonically conjugate functionals (one being the field probability density). The postulate that a classical ensemble is subject to nonclassical fluctuations of…
We review some essential aspects of classically integrable systems. The detailed outline of the lectures consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples…
The problem of characterising the accuracy of, and disturbance caused by a joint measurement of position and momentum is investigated. In a previous paper the problem was discussed in the context of the unbiased measurements considered by…
We shed new light on Heisenberg's uncertainty principle in the sense of Beurling, by offering an essentially different proof which permits us to weaken the assumptions substantially, and examples show that the result is sharp. The proof…
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…
Fourier analysis on the discrete hypercubes $\{-1,1\}^n$ has found numerous applications in learning theory. A recent breakthrough involves the use of a classical result from Fourier analysis, the Bohnenblust--Hille inequality, in the…
Uncertainty principle, a fundamental principle in quantum physics, has been studied intensively via various uncertainty inequalities. Here we derive an uncertainty equality in terms of linear entropy, and show that the sum of uncertainty in…
This paper presents a novel numerical method for the hybrid reliability analysis by using the uncertainty theory. Aleatory uncertainty and epistemic uncertainty are considered simultaneously in this method. Epistemic uncertainty is…
Signal recovery from incomplete or partial frequency information is a fundamental problem in harmonic analysis and applied mathematics, with wide-ranging applications in communications, imaging, and data science. Historically, the classical…
Let $G$ be a finite abelian group. Let $f: G \to {\mathbb C}$ be a signal (i.e. function). The classical uncertainty principle asserts that the product of the size of the support of $f$ and its Fourier transform $\hat f$, $\text{supp}(f)$…
The purpose of this article is to survey certain aspects of multilinear harmonic analysis related to notions of transversality. Particular emphasis will be placed on the multilinear restriction theory for the euclidean Fourier transform,…
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…
This paper investigates the mathematical nature of qualitative uncertainty principle (QUP), which plays an important role in mathematics, physics and engineering fields. Consider a 3-tuple (K, H1, H2) that K: H1 -> H2 is an integral…
We develop a new approach to estimate the uncertainty due to missing higher orders in perturbative predictions (the perturbative "theory uncertainty"), which overcomes many inherent limitations of the currently prevalent methods based on…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
In this paper, we uncover a new uncertainty principle that governs the complexity of Boolean functions. This principle manifests as a fundamental trade-off between two central measures of complexity: a combinatorial complexity of its…