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2 results on '"Gelfand–Levitan–Marchenko equations"'

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

Author

Kopylova, Elena and Teschl, Gerald

Subjects
*DIRAC equation, *DIRAC operators, *REFLECTANCE, *DISPERSION (Chemistry), *S-matrix theory
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. [ABSTRACT FROM AUTHOR]

Published
2022
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2. Scattering properties and dispersion estimates for a one‐dimensional discrete Dirac equation

Author

Elena Kopylova and Gerald Teschl

Subjects
General Mathematics, Gelfand–Levitan–Marchenko equations, FOS: Physical sciences, Mathematical Physics (math-ph), discrete Dirac equation, Mathematics - Spectral Theory, Primary 35Q41, 81Q15, Secondary 39A12, 39A70, FOS: Mathematics, dispersive decay, Wiener algebra, Spectral Theory (math.SP), Mathematical Physics, Jost solutions, scattering matrix
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., 18 pages

Published
2022

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