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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Veröffentlicht in:Linear algebra and its applications Jg. 389; S. 305 - 322
Hauptverfasser: Belyi, Sergey, Tsekanovskii, Eduard
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY Elsevier Inc 15.09.2004
Elsevier Science
Schlagworte:
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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Zusammenfassung: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2004.04.002