On a formula of the generalized resolvents of a nondensely defined Hermitian operator

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1992 English Publisher:Springer Science and Business Media LLCJournal:Ukrainian Mathematical Journal, volume 44, pages 1,522-1,547 (issn: 0041-5995, eissn: 1573-9376,

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Authors: M. M. Malamud;

doi: 10.1007/bf01061278

On a formula of the generalized resolvents of a nondensely defined Hermitian operator

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Abstract

The Weyl function and the prohibited lineal, corresponding to a given space of boundary values of a nondensely defined Hermitian operator, are introduced and investigated. The prohibited lineal is characterized in terms of the limiting values of the Weyl function. An analogue of M. G. Krein's formula for the resolvent is obtained and its connection with the space of boundary values is found.

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Donetsk National Technical University
Ukraine

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