BooksecrCollected Volumepp. 95–127

On the index of meromorphic operator-valued functions and some applications

  • Jussi Behrndt

    TU Graz, Austria
  • Fritz Gesztesy

    Baylor University, Waco, USA
  • Helge Holden

    University of Trondheim, Norway
  • Roger Nichols

    The University of Tennessee at Chattanooga, USA
On the index of meromorphic operator-valued functions and some applications cover
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Abstract

We revisit and connect several notions of algebraic multiplicities of zeros of analytic operator-valued functions and discuss the concept of the index of meromorphic operator-valued functions in complex, separable Hilbert spaces. Applications to abstract perturbation theory and associated Birman–Schwinger-type operators and to the operator-valued Weyl–Titchmarsh functions associated to closed extensions of dual pairs of closed operators are provided.