Dispersive Properties for Discrete Schrodinger Equations

TL;DR

This paper establishes dispersive estimates for coupled discrete Schrödinger equations, demonstrating decay properties of solutions through resolvent analysis and oscillatory integral techniques.

Contribution

It provides the first dispersive estimates for coupled discrete Schrödinger systems, including resolvent bounds and limiting absorption principles.

Findings

Proved dispersive decay estimates for coupled discrete Schrödinger equations

Established resolvent estimates satisfying the limiting absorption principle

Applied oscillatory integral methods to analyze solution decay

Abstract

In this paper we prove dispersive estimates for the system formed by two coupled discrete Schr\"odinger equations. We obtain estimates for the resolvent of the discrete operator and prove that it satisfies the limiting absorption principle. The decay of the solutions is proved by using classical and some new results on oscillatory integrals.