The Krein formula in almost Pontryagin spaces. A proof via orthogonal coupling

Henk de Snoo; Harald Woracek

doi:10.1016/j.indag.2017.12.001

The Krein formula in almost Pontryagin spaces. A proof via orthogonal coupling

Henk de Snoo^*, Harald Woracek

^*Corresponding author for this work

Dynamical Systems, Geometry and Mathematical Physics

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Abstract

A new proof is provided for the Krein formula for generalized resolvents in the context of symmetric operators or relations with defect numbers (1, 1) in an almost Pontryagin space. The new proof is geometric and uses the orthogonal coupling of the almost Pontryagin spaces induced by the Q-function and the parameter function in the Krein formula. (C) 2017 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	714-729
Number of pages	16
Journal	Indagationes mathematicae-New series
Volume	29
Issue number	2
DOIs	https://doi.org/10.1016/j.indag.2017.12.001
Publication status	Published - Apr-2018

Keywords

Almost Pontryagin space
Krein's formula
Orthogonal coupling
Generalized resolvent
GENERALIZED RESOLVENTS
SYMMETRIC-OPERATORS

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10.1016/j.indag.2017.12.001

The Krein formula in almost Pontryagin spaces. A proof via orthogonal couplingFinal publisher's version, 349 KBLicence: Taverne

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abstract = "A new proof is provided for the Krein formula for generalized resolvents in the context of symmetric operators or relations with defect numbers (1, 1) in an almost Pontryagin space. The new proof is geometric and uses the orthogonal coupling of the almost Pontryagin spaces induced by the Q-function and the parameter function in the Krein formula. (C) 2017 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.",

keywords = "Almost Pontryagin space, Krein's formula, Orthogonal coupling, Generalized resolvent, GENERALIZED RESOLVENTS, SYMMETRIC-OPERATORS",

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AU - Woracek, Harald

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N2 - A new proof is provided for the Krein formula for generalized resolvents in the context of symmetric operators or relations with defect numbers (1, 1) in an almost Pontryagin space. The new proof is geometric and uses the orthogonal coupling of the almost Pontryagin spaces induced by the Q-function and the parameter function in the Krein formula. (C) 2017 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

AB - A new proof is provided for the Krein formula for generalized resolvents in the context of symmetric operators or relations with defect numbers (1, 1) in an almost Pontryagin space. The new proof is geometric and uses the orthogonal coupling of the almost Pontryagin spaces induced by the Q-function and the parameter function in the Krein formula. (C) 2017 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

KW - Almost Pontryagin space

KW - Krein's formula

KW - Orthogonal coupling

KW - Generalized resolvent

KW - GENERALIZED RESOLVENTS

KW - SYMMETRIC-OPERATORS

U2 - 10.1016/j.indag.2017.12.001

DO - 10.1016/j.indag.2017.12.001

M3 - Article

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VL - 29

SP - 714

EP - 729

JO - Indagationes mathematicae-New series

JF - Indagationes mathematicae-New series

IS - 2

ER -

The Krein formula in almost Pontryagin spaces. A proof via orthogonal coupling

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Keywords

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