Related papers: Uncertainty principles and singular potentials

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…

We show how a number of well-known uncertainty principles for the Fourier transform, such as the Heisenberg uncertainty principle, the Donoho--Stark uncertainty principle, and Meshulam's non-abelian uncertainty principle, have little to do…

For the Szekeres system which describes inhomogeneous and anisotropic spacetimes we make use of a point-like Lagrangian, which describes the evolution of the physical variables of the Szekeres model, in order to perform a canonical…

By using the local dimension-free Harnack inequality established on incomplete Riemannian manifolds, integrability conditions on the coefficients are presented for SDEs to imply the non-explosion of solutions as well as the existence,…

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…

We prove a new version of the Uncertainty Principle of the form $\int |f|^2 \lesssim \int_{E^c} |f|^2 + \int_{\Sigma ^c}|\hat f|^2 $ where the sets $E$ and $\Sigma$ are $\epsilon$-thin in the following sense: $|E \cap D(x, \rho_1(x))| \le…

Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures that are independent in some sense. This yields…

We derive explicit bounds for the remainder term in the local Weyl law for locally hyperbolic manifolds, we also give the estimates of the derivative of this remainder. We use these to obtain explicit bounds for the C^k-norms of the…

In this paper, we prove some a priori stability estimates (in weighted Sobolev spaces) for the spatially homogeneous Boltzmann equation without angular cutoff (covering every physical collision kernels). These estimates are conditioned to…

This is the first paper of a series in which we plan to study spectral asymptotics for sub-Riemannian Laplacians and to extend results that are classical in the Riemannian case concerning Weyl measures, quantum limits, quantum ergodicity,…

The spectrum of the singular indefinite Sturm-Liouville operator $$A=\text{\rm sgn}(\cdot)\bigl(-\tfrac{d^2}{dx^2}+q\bigr)$$ with a real potential $q\in L^1(\mathbb R)$ covers the whole real line and, in addition, non-real eigenvalues may…

First we prove a general spectral theorem for the linear Navier-Stokes (NS) operator in both 2D and 3D. The spectral theorem says that the spectrum consists of only eigenvalues which lie in a parabolic region, and the eigenfunctions (and…

In this work, we study compact Riemannian manifolds with boundary satisfying V-static-type equations. By combining a generalized Reilly formula with Steklov-type boundary value problems, we derive integral inequalities for geometric…

It has been known since the work of Avakumov\'ic, H\"ormander and Levitan that, on any compact smooth Riemannian manifold, if $-\Delta_g \psi_\lambda = \lambda \psi_\lambda$, then $\|\psi_\lambda\|_{L^\infty} \leq C \lambda^{\frac{d-1}{4}}…

In this paper, we prove the anisotropic Shannon inequality for the Renyi entropy with the best constant on Folland-Stein homogeneous Lie groups. As a consequence, we also prove the optimal Shannon inequality in the same setting. Using a…

We present a unified representation-theoretic method to compute the Laplace-Beltrami spectrum on homogeneous principal bundles. For this setting, we introduce a multi-parameter family of metric deformations called generalized canonical…

We study the Heisenberg-Pauli-Weyl uncertainty principle and the Caffarelli-Kohn-Nirenberg interpolation inequalities, on metric measure spaces satisfying measure contraction property. Using localization techniques, we show that these…

In this paper, we study the two-point Weyl Law for the Laplace-Beltrami operator on a smooth, compact Riemannian manifold $M$ with no conjugate points. That is, we find the asymptotic behavior of the Schwartz kernel, $E_\lambda(x,y)$, of…

Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…

We prove multipolar Hardy inequalities on complete Riemannian manifolds, providing various curved counterparts of some Euclidean multipolar inequalities due to Cazacu and Zuazua [Improved multipolar Hardy inequalities, 2013]. We notice that…