On Krein's formula in indefinite metric spaces

In this paper we extend some of the recent results in connection with the Krein resolvent formula which provides a complete description of all canonical resolvents and utilizes Weyl–Titchmarsh functions in the spaces with indefinite metrics. We show that coefficients in Krein's formula can be e...

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Vydané v:	Linear algebra and its applications Ročník 389; s. 305 - 322
Hlavní autori:	Belyi, Sergey, Tsekanovskii, Eduard
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York, NY Elsevier Inc 15.09.2004 Elsevier Science
Predmet:	Algebra Exact sciences and technology Indefinite metrics Krein's formula Linear and multilinear algebra, matrix theory Mathematics Pontryagin space Sciences and techniques of general use Pontryagin space Indefinite metrics Krein's formula Neumann problem Resolvent Metric space Indefinite metric Parameterization Linear transformation
ISSN:	0024-3795, 1873-1856
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Abstract	In this paper we extend some of the recent results in connection with the Krein resolvent formula which provides a complete description of all canonical resolvents and utilizes Weyl–Titchmarsh functions in the spaces with indefinite metrics. We show that coefficients in Krein's formula can be expressed in terms of analogues of the von Neumann parametrization formulas in the indefinite case. We consider properties of Weyl–Titchmarsh functions and show that two Weyl–Titchmarsh functions corresponding to π-self-adjoint extensions of a densely defined π-symmetric operator are connected via linear-fractional transformation with the coefficients presented in terms of von Neumann's parameters.
AbstractList	In this paper we extend some of the recent results in connection with the Krein resolvent formula which provides a complete description of all canonical resolvents and utilizes Weyl–Titchmarsh functions in the spaces with indefinite metrics. We show that coefficients in Krein's formula can be expressed in terms of analogues of the von Neumann parametrization formulas in the indefinite case. We consider properties of Weyl–Titchmarsh functions and show that two Weyl–Titchmarsh functions corresponding to π-self-adjoint extensions of a densely defined π-symmetric operator are connected via linear-fractional transformation with the coefficients presented in terms of von Neumann's parameters.
Author	Tsekanovskii, Eduard Belyi, Sergey
Author_xml	– sequence: 1 givenname: Sergey surname: Belyi fullname: Belyi, Sergey email: sbelyi@trojan.troyst.edu organization: Department of Mathematics, Troy State University, Troy, AL 36082, USA – sequence: 2 givenname: Eduard surname: Tsekanovskii fullname: Tsekanovskii, Eduard email: tsekanov@niagara.edu organization: Department of Mathematics, Niagara University, NY 14109, USA
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Keywords	Pontryagin space Indefinite metrics Krein's formula Neumann problem Resolvent Metric space Indefinite metric Parameterization Linear transformation
Language	English
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Snippet	In this paper we extend some of the recent results in connection with the Krein resolvent formula which provides a complete description of all canonical...
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SubjectTerms	Algebra Exact sciences and technology Indefinite metrics Krein's formula Linear and multilinear algebra, matrix theory Mathematics Pontryagin space Sciences and techniques of general use
Title	On Krein's formula in indefinite metric spaces
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