Related papers: Dynamical versions of Hardy's uncertainty principl…
We establish a quantitative relation between Hardy's paradox and the breaking of uncertainty principle in the sense of measurement-disturbance relations in the conditional measurement of non-commuting operators. The analysis of the…
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 discuss the relation between density matrices and the uncertainty principle; this allows us to justify and explain a recent statement by Man'ko et al. We thereafter use Hardy's uncertainty principle to prove a new result for Wigner…
We study the process of dispersion of low-regularity solutions to the Schr\"odinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get a lower bound…
For absolutely convergent series we state explicitly a one-sided summation estimate that can be viewed as the discrete analogue of the change of variable formula on the half line. This estimate is implicit in Pascal Lef\`evre's recent…
In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the Clifford-Fourier transform on $\mathbb{R}^m$.
Hardy's proof is considered the simplest proof of nonlocality. Here we introduce an equally simple proof that (i) has Hardy's as a particular case, (ii) shows that the probability of nonlocal events grows with the dimension of the local…
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…
Depending on the way one measures, quantum nonlocality might manifest more visibly. Using basis transformations and interactions on a particle pair, Hardy logically argued that any local hidden variable theory leads to a paradox. Extended…
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…
In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the two-sided quaternion Fourier transform.
The aim of this paper is to prove two new uncertainty principles for the Fourier-Bessel transform (or Hankel transform). The first of these results is an extension of a result of Amrein-Berthier-Benedicks, it states that a non zero function…
In this paper, Hardy's uncertainty principle and unique continuation properties of abstract Schr\"odinger equations in vector-valued classes are obtained
In this work, we summarize the linearization method to study the Heisenberg Uncertainty Principles, and explain that the same approach can be used to handle the stability problem. As examples of application, combining with spherical…
The aim of this paper is two prove two versions of the Dynamical Uncertainty Principlefor the Schr\"odinger equation $i\partial_s u=\mathcal{L}u+Vu$, $u(s=0)=u_0$ where$\mathcal{L}$ is the sub-Laplacian on the Heisenberg group.We show two…
We consider the Hardy constant associated with a domain in the $n$-dimensional Euclidean space and we study its variation upon perturbation of the domain. We prove a Fr\'{e}chet differentiability result and establish a Hadamard-type formula…
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)…
Classical results due to Ingham and Paley-Wiener characterize the existence of nonzero functions supported on certain subsets of the real line in terms of the pointwise decay of the Fourier transforms. We view these results as uncertainty…
We consider the $L^p$ Hardy inequality involving the distance to the boundary for a domain in the $n$-dimensional Euclidean space. We study the dependence on $p$ of the corresponding best constant and we prove monotonicity, continuity and…
In this paper, we study the uncertainty principle for Schr\"odinger equations with a bounded time-independent potentials on certain Cartan-Hadamard manifolds endowed with an asymptotic hyperbolic metric in dimensions $n\geq2$. The classical…