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dc.contributor.authorJonas, Peter
dc.description.abstractLet $\Omega$ be some domain in $\overline{{\bf C}}$ symmetric with respect to the real axis and such that $\Omega \cap \overline{{\bf R}} \neq \emptyset$ and the intersections of $\Omega$ with the upper and lower open half-planes are simply connected. We study the class of piecewise meromorphic ${\bf R}$-symmetric operator functions $G$ in $\Omega \setminus \overline{{\bf R}}$ such that for any subdomain $\Omega'$ of $\Omega$ with $\overline{\Omega'} \subset \Omega$, $G$ restricted to $\Omega'$ can be written as a sum of a definitizable and a (in $\Omega'$) holomorphic operator function. As in the case of a definitizable operator function, for such a function $G$ we define intervals $\Delta \subset {\bf R} \cap \Omega$ of positive and negative type as well as some ``local'' inner products associated with intervals $\Delta \subset {\bf R} \cap \Omega$. Representations of $G$ with the help of linear operators and relations are studied, and it is proved that there is a representing locally definitizable selfadjoint relation $A$ in a Krein space which locally exactly reflects the sign properties of $G$: The ranks of positivity and negativity of the spectral subspaces of $A$ coincide with the numbers of positive and negative squares of the "local'' inner products corresponding to $G$.en
dc.subject.ddc510 Mathematiken
dc.subject.otherdefinitizable operator functionsen
dc.subject.othergeneralized Nevanlinna functionsen
dc.subject.otherselfadjoint and unitary operators in Krein spacesen
dc.subject.otherlocally definitizable operatorsen
dc.subject.otherspectral points of positive and negative typeen
dc.titleOn operator representations of locally definitizable functionsen
dc.typeResearch Paperen
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2005, 20en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften » Inst. Mathematikde
tub.subject.msc200047B50 Operators on spaces with an indefinite metricen
tub.subject.msc200047A56 Functions whose values are linear operatorsen
tub.subject.msc200047A60 Functional calculusen
Appears in Collections:Technische Universität Berlin » Publications

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