Scattering properties and dispersion estimates for a one-dimensional discrete Dirac equation

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.

Automated summary

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. Moreover, we provide new results concerning scattering for the corresponding perturbed Dirac operators, showing that the reflection and transmission coefficients belong to the Wiener algebra.