Scattering properties and dispersion estimates for a one‐dimensional discrete Dirac equation. Issue 4 (7th March 2022)

• Record Type: Journal Article
• Authors: Kopylova, Elena; Teschl, Gerald
• Is Part Of: Mathematische Nachrichten. Volume 295:Issue 4(2022)
• Page Start: 762
• Page End: 784
• Publication Date: 2022-03-07
• Subjects: discrete Dirac equation -- dispersive decay -- Gelfand–Levitan–Marchenko equations -- Jost solutions -- scattering matrix -- Wiener algebra; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.202000033
• Languages: English
• ISSNs: 0025-584X

Abstract

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.