Uniqueness Properties for Discrete equations and Carleman estimates

TL;DR

This paper uses Carleman estimates to establish lower bounds and uniqueness results for solutions of the discrete Schrödinger equation, considering both dynamic and stationary cases with specific decay conditions.

Contribution

It introduces a novel approach applying Carleman estimates to discrete Schrödinger equations to derive new uniqueness theorems under decay assumptions.

Findings

Established lower bounds for solutions using Carleman estimates

Proved uniqueness results for solutions with decay conditions

Applicable to both dynamic and stationary discrete Schrödinger equations

Abstract

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