Uniqueness Properties for Discrete equations and Carleman estimates

Abstract

Using Carleman estimates, we give a lower bound for solutions to the discrete Schrödinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions.

In the revised version, published in 2017, we improve our Carleman estimate and the method of proof of Theorem 1.1 in order to quantify the uniqueness result in the one dimensional case, proving the sharp uniqueness result conjectured by Lyubarskii, Jaming, Malinnikova and Perfekt