相关论文: Uncertainty principle for the Poly-axially L 2 {\a…

In this paper, we generalise Hardy's uncertainty principle to vector-valued functions, and hence to operators. The principle for operators can be formulated loosely by saying that the kernel of an operator cannot be localised near the…

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…

This paper originates from a naive attempt to establish various non-commutative Fourier theoretic inequalities for an inclusion of simple C*-algebras equipped with a conditional expectation of index-finite type. In this setting, we discuss…

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…

Recently Kosaki proved an uncertainty principle for matrices, related to Wigner-Yanase-Dyson information, and asked if a similar inequality could be proved in the von Neumann algebra setting. In this paper we prove such an uncertainty…

This paper presents a proof of an uncertainty principle of Donoho-Stark type involving $\varepsilon$-concentration of localization operators. More general operators associated with time-frequency representations in the Cohen class are then…

We revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of…

In this paper, we introduce the notation of bi-shift of biprojections in subfactor theory to unimodular Kac algebras. We characterize the minimizers of Hirschman-Beckner uncertainty principle and Donoho-Stark uncertainty principle for…

The aim of this paper is to derive a new uncertainty principle for the generalized $q$-Bessel wavelet transform studied earlier in \cite{Rezguietal}. In this paper, an uncertainty principle associated with wavelet transforms in the…

Let $G$ be a locally compact abelian group, and let $\widehat{G}$ denote its dual group, equipped with a Haar measure. A variant of the uncertainty principle states that for any $S \subset G$ and $\Sigma \subset \widehat{G}$, there exists a…

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…

This paper focuses on studying the Donoho-Stark's type uncertainty principle for the continuous Clifford wavelet transform. A brief review of Clifford algebra/analysis, Clifford wavelet transform and their properties is conducted. Next,…

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…

For any ideal two-path interferometer it is shown that the wave-particle duality of quantum mechanics implies Heisenberg's uncertainty relation and vice versa. It is conjectured that complementarity and uncertainty are two aspects of the…

Let $G$ be a finite abelian group. If $f: G\rightarrow \bC$ is a nonzero function with Fourier transform $\hf$, the Donoho-Stark uncertainty principle states that $|\supp(f)||\supp(\hf)|\geq |G|$. The purpose of this paper is twofold.…

We obtain a new version of the Uncertainty Principle for functions with Fourier transforms supported on a lacunary set of intervals. This is a generalization of Zygmund's theorem on lacunary trigonometric series to the real line in the…

We consider a class of fully nonlinear integro-differential operators where the nonlocal integral has two components: the non-degenerate one corresponds to the $\alpha$-stable operator and the second one (possibly degenerate) corresponds to…

In this paper we have generalized and studied the $K$-Weyl-Heisenberg frames, where $K$ is a bounded linear operator on $L^2(\mathbb{R}^d)$. We have obtained necessary and sufficient conditions for acertain system to be a…

New position uncertainty (delocalization) measures for a particle on the circle are proposed and illustrated on several examples, where the previous measures (based on 2pi-periodic position operators) appear to be unsatisfactory. The new…

The admittable Sobolev regularity is quantified for a function, $w$, which has a zero in the $d$--dimensional torus and whose reciprocal $u=1/w$ is a $(p,q)$--multiplier. Several aspects of this problem are addressed, including zero--sets…