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Completion problems and scattering problems for Dirac type differential equations with singularities |
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| Authors: | Bernd Fritzsche Alexander Sakhnovich |
| Affiliation: | a Fakultät für Mathematik und Informatik, Mathematisches Institut, Universität Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany b Branch of Hydroacoustics, Marine Institute of Hydrophysics, National Academy of Sciences, Preobrazhenskaya 3, Odessa, Ukraine |
| Abstract: | A completion problem to recover a rational matrix function which is j-unitary on the line is treated. A Dirac type system with singularities on the semi-axis is recovered explicitly from its left reflection coefficient. The close relation between these two problems is discussed. |
| Keywords: | Completion problem Dirac type system Scattering problem Reflection coefficient Realization Arov-singular matrix function Positon type potential |
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