On Uniqueness Properties of Solutions of Schrödinger Equations

Hardy's uncertainty principle, convexity and Schrödinger evolutions

“…In this paper we continue the study initiated in [11] and [2] on unique continuation properties of solutions of Schrödinger evolutions…”

“…In our previous paper [2] we proved a uniqueness result in this direction for potentials which satisfy (1.2) lim…”

“…Our improvement for the results of [2] comes from a better understanding of the solutions to (1.1), which have a Gaussian decay. We started the study of this particular type of solutions in our recent work [3], where we consider free waves (i.e.…”

On the decay properties of solutions to a class of Schrödinger equations

“…We observe that in formula (1.5), the positive and negative frequencies do not interact and, also, that u(x, t) := e −βx v(x, t) is not necessarily an L 2 -solution of the free Schrödinger equation. The following estimate established in [7] of the type described in (1.6) for a linear Schrödinger equation with lower order variable coefficients (1.2) (b) was a key step in the proof of the unique continuation results obtained in [7] and [4].…”

A dynamic uncertainty principle for Jacobi operators

“…The Hardy Uncertainty Principle has been studied by several authors in the continuous case, see for example the monograph [7] or the recent articles [1,2] and the references therein. The dynamic version for the free Schrödinger equation says that if u(t, x) is a solution of ∂ t u = i∆u and |u(0, x)| = O(e [3,4,5,6,8].…”