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On Weyl function and generalized resolvents of a Hermitian operator in a Krein space

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Abstract

A description of generalized resolvents for a densely defined Hermitian operatorA in a Krein space\(\mathcal{K}\) is given under explicit consideration of the number of negative squares of the inner product on the extending space

and of the forms [A·,·], [A·,·],A being a selfadjoint extension ofA which corresponds to the generalized resolvent. New classesN κ k of analytic functions are introduced for this purpose. An application to a Sturm-Liouville operator with indefinite weight function is discussed.

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Authors and Affiliations

  1. Department of Mathematics, Donetsk University, Universitetskaya str. 24, 340055, Donetsk, Ukraine

    V. Derkach

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The author thanks the TU Berlin for the hospitallity and financial support

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Derkach, V. On Weyl function and generalized resolvents of a Hermitian operator in a Krein space. Integr equ oper theory 23, 387–415 (1995). https://doi.org/10.1007/BF01203914

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