On the index of meromorphic operator-valued functions and some applications
Jussi Behrndt
TU Graz, AustriaFritz Gesztesy
Baylor University, Waco, USAHelge Holden
University of Trondheim, NorwayRoger Nichols
The University of Tennessee at Chattanooga, USA
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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.