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An Uncertainty Principle for Solutions of the Schrödinger Equation on H-Type Groups
(Cambridge University Press, 2020-04-02)
In this paper we consider uncertainty principles for solutions of certain partial differential equations on H -type groups. We first prove that, on H -type groups, the heat kernel is an average of Gaussians in the central ...
Hardy's uncertainty principle and unique continuation property for stochastic heat equations
(EDP Sciences, 2020-02-14)
The goal of this paper is to prove a qualitative unique continuation property at two points in time for a stochastic heat equation with a randomly perturbed potential, which can be considered as a variant of Hardy’s ...
From Heisenberg uniqueness pairs to properties of the Helmholtz and Laplace equations
(Elsevier, 2018-09-07)
The aim of this paper is to establish uniqueness properties of solutions of the Helmholtz and Laplace equations. In particular, we show that if two solutions of such equations on a domain of Rd agree on two intersecting d ...
Uniqueness for solutions of the Schrödinger equation on trees
(Fondazione Annali di Matematica Pura ed Applicata and Springer Nature, 2019-08-30)
We prove that if a solution of the time-dependent Schrödinger equation on an homogeneous tree with bounded potential decays fast at two distinct times then the solution is trivial. For the free Schrödinger operator, we use ...
Convexity properties of discrete Schrödinger evolutions
(Springer Nature, 2019-07-01)
In this paper, we give log-convexity properties for solutions to discrete Schrödinger equations with different discrete versions of Gaussian decay at two different times. For free evolutions, we use complex analysis arguments ...