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

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 o...

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Bibliographic Details
Published in:Mathematische Nachrichten Vol. 295; no. 4; pp. 762 - 784
Main Authors: Kopylova, Elena, Teschl, Gerald
Format: Journal Article
Language:English
Published: Weinheim Wiley Subscription Services, Inc 01-04-2022
Subjects:
Dirac equation
discrete Dirac equation
Dispersion
dispersive decay
Estimates
Gelfand–Levitan–Marchenko equations
Jost solutions
Mathematical analysis
Operators (mathematics)
Scattering
scattering matrix
Wiener algebra
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Description
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. 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.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202000033