Article
Math. Nachr. 295, 762-784 (2022) [DOI: 10.1002/mana.202000033]

Scattering Properties and Dispersion Estimates for a One-Dimensional Discrete Dirac Equation

Elena Kopylova and Gerald Teschl

Abstract
We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results concerning scattering for the corresponding perturbed Dirac operators which are of independent interest. Most notably, we show that the reflection and transmission coefficients belong to the Wiener algebra.

MSC2010: Primary 35Q41, 81Q15; Secondary 39A12, 39A70
Keywords: Discrete Dirac equation, Jost solutions, scattering matrix, Gelfand-Levitan-Marchenko equations, Wiener algebra, dispersive decay

Download
TeX file (76k) or pdf file (374k)