Dispersion Estimates for One-Dimensional Discrete Dirac Equations

TL;DR

This paper develops dispersion estimates for solutions to the one-dimensional discrete Dirac equation by establishing scattering theory and a limiting absorption principle for perturbed operators.

Contribution

It introduces a novel approach to derive dispersion estimates for discrete Dirac equations using scattering theory and the limiting absorption principle.

Findings

Established dispersion estimates for discrete Dirac equations.

Developed scattering theory for discrete perturbed Dirac operators.

Proved a limiting absorption principle for these operators.

Abstract

We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Dirac equation. To this end we develop basic scattering theory and establish a limiting absorption principle for discrete perturbed Dirac operators.