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Author: Neidhardt, Hagen × End date: 2009 × Start date: 2000 × DDC: 510 × Has files: Yes × Type: Text × Subject: Scattering system ×

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Now showing 1 - 3 of 3
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    Scattering matrices and Weyl functions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Behrndt, Jussi; Malamud, Mark M.; Neidhardt, Hagen
    For a scattering system consisting of two selfadjoint extensions of a symmetric operator A with finite deficiency indices, the scattering matrix and the spectral shift function are calculated in terms of the Weyl function associated with the boundary triplet for A* and a simple proof of the Krein-Birman formula is given. The results are applied to singular Sturm-Liouville operators with scalar- and matrix-valued potentials, to Dirac operators and to Schroedinger operators with point interactions.
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    Finite rank perturbations, scattering matrices and inverse problems : dedicated to the memory of our friend Peter Jonas (18.7.1941 - 18.7.2007)
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Behrndt, Jussi; Malamud, Mark M.; Neidhardt, Hagen; Jonas, Peter
    In this paper the scattering matrix of a scattering system consisting of two selfadjoint operators with finite dimensional resolvent difference is expressed in terms of a matrix Nevanlinna function. The problem is embedded into an extension theoretic framework and the theory of boundary triplets and associated Weyl functions for (in general nondensely defined) symmetric operators is applied. The representation results are extended to dissipative scattering systems and an explicit solution of an inverse scattering problem for the Lax-Phillips scattering matrix is presented.
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    Trace formulae for dissipative and coupled scattering systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Behrndt, Jussi; Malamud, Mark; Neidhardt, Hagen
    For scattering systems consisting of a (family of) maximal dissipative extension(s) and a selfadjoint extension of a symmetric operator with finite deficiency indices, the spectral shift function is expressed in terms of an abstract Titchmarsh-Weyl function and a variant of the Birman-Krein formula is proved.