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- ItemScattering matrices and Dirichlet-to-Neumann maps(Amsterdam [u.a.] : Elsevier, 2017) Behrndt, Jussi; Malamud, Mark M.; Neidhardt, HagenA general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator valued Titchmarsh–Weyl m-function is proved. This result is applied to scattering problems for different self-adjoint realizations of Schrödinger operators on unbounded domains, Schrödinger operators with singular potentials supported on hypersurfaces, and orthogonal couplings of Schrödinger operators. In these applications the scattering matrix is expressed in an explicit form with the help of Dirichlet-to-Neumann maps.
- ItemScattering matrices and Weyl functions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Behrndt, Jussi; Malamud, Mark M.; Neidhardt, HagenFor 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.