Finite rank perturbations, scattering matrices and inverse problems : dedicated to the memory of our friend Peter Jonas (18.7.1941 - 18.7.2007)

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.

Keywords

Scattering system, scattering matrix, boundary triplet, Weyl function, dissipative operator, Lax-Phillips scattering

URI

https://doi.org/10.34657/2394
https://oa.tib.eu/renate/handle/123456789/2112

Citation

Behrndt, J., Malamud, M. M., Neidhardt, H., & Jonas, P. (2009). Finite rank perturbations, scattering matrices and inverse problems : dedicated to the memory of our friend Peter Jonas (18.7.1941 - 18.7.2007) (Vol. 1406). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.

Collections

Mathematik

License

This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.

Full item page