- 09-27 Jussi Behrndt, Mark M. Malamud, Hagen Neidhardt
- Finite Rank Perturbations, Scattering Matrices and
Inverse Problems
(383K, pdf)
Feb 20, 09
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Abstract. 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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