WIAS Preprint No. 1121, (2006)

Scattering matrices and Weyl functions



Authors

  • Behrndt, Jussi
  • Malamud, Mark M.
  • Neidhardt, Hagen

2010 Mathematics Subject Classification

  • 47B50

Keywords

  • scattering system, scattering matrix, boundary triplet, (Titchmarsh-) Weyl function, spectral shift function, Krein-Birman formula, Sturm-Liouville operator, Dirac operator, Schroedinger operator

Abstract

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.

Appeared in

  • Proc. London Math. Soc. (3), 97 (2008) pp. 568--598.

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