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Main Title: Boundary Relations and Generalized Resolvents of Symmetric Operators in Krein Spaces
Author(s): Behrndt, Jussi
Kreusler, Hans-Christian
Type: Research Paper
Abstract: The classical Krein-Naimark formula establishes a one-to-one correspondence between the generalized resolvents of a closed symmetric operator in a Hilbert space and the class of Nevanlinna families in a parameter space. Recently it was shown by V.A. Derkach, S. Hassi, M.M. Malamud and H.S.V. de Snoo that these parameter families can be interpreted as so-called Weyl families of boundary relations, and a new proof of the Krein-Naimark formula in the Hilbert space setting was given with the help of a coupling method. The main objective of this paper is to generalize the notion of boundary relations and their Weyl families to the Krein space case and to proof some variants of the Krein-Naimark formula in an indefinite setting.
Subject(s): symmetric operator
self-adjoint extension
Krein-Naimark formula
generalized resolvent
boundary relation
boundary triplet
(locally) definitizable operator
Krein space
Issue Date: 11-Sep-2006
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 47B50 Operators on spaces with an indefinite metric
47A20 Dilations, extensions, compressions
47B25 Symmetric and selfadjoint operators
46C20 Spaces with indefinite inner product
47A06 Linear relations
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2006, 33
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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