Scattering for general-type Dirac systems on the semi-axis: reflection coefficients and Weyl functions

2018/01/30 by Alexander Sakhnovich · 1 citation
Mathematics · Physics and Astronomy · #math.SP #math-ph #math.CA #math.MP #msc:34A55 #msc:34B20 #msc:34L25 #msc:34A05

paper · pdf · doi:10.1016/j.jde.2018.06.024

published as J. Differential Equations 265 (2018), pp. 4820--4834

arxiv created 2018/01/30 · arxiv updated 2020/07/03

Abstract

We show that for general-type self-adjoint and skew-self-adjoint Dirac systems on the semi-axis Weyl functions are unique analytic extensions of the reflection coefficients. New results on the extension of the Weyl functions to the real axis and on the existence (in the skew-self-adjoint case) of the Weyl functions follow. Important procedures to recover general-type Dirac systems from the Weyl functions are applied to the recovery of Dirac systems from the reflection coefficients. We explicitly recover Dirac systems from the rational reflection coefficients as well.

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• Discrete Dirac systems on the semiaxis: rational reflection coefficients and Weyl functions

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