Scattering matrices and Weyl functions
- Behrndt, Jussi
- Malamud, Mark M.
- Neidhardt, Hagen
2010 Mathematics Subject Classification
- scattering system, scattering matrix, boundary triplet, (Titchmarsh-) Weyl function, spectral shift function, Krein-Birman formula, Sturm-Liouville operator, Dirac operator, Schroedinger operator
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.
- Proc. London Math. Soc. (3), 97 (2008) pp. 568--598.