WIAS Preprint No. 1282, (2007)

Trace formulae for dissipative and coupled scattering systems



Authors

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

2010 Mathematics Subject Classification

  • 47A40 47A55 47B44

Keywords

  • Scattering system, scattering matrix, boundary triplet, Titchmarsh-Weyl function, spectral shift function, Krein-Birman formula

Abstract

For scattering systems consisting of a (family of) maximal dissipative extension(s) and a selfadjoint extension of a symmetric operator with finite deficiency indices, the spectral shift function is expressed in terms of an abstract Titchmarsh-Weyl function and a variant of the Birman-Krein formula is proved.

Appeared in

  • vol. 188 of Operator Theory: Advances and Applications, Birkhäuser, Basel, 2008, pp. 57--93

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