On Krein's formula

Jussi Behrndt; Henk de Snoo

doi:10.1016/j.jmaa.2008.10.046

On Krein's formula

Jussi Behrndt^*, Henk de Snoo

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

4 Citations (Scopus)

Abstract

Krein's formula provides a parametrization of the generalized resolvents and Straus extensions of a closed symmetric operator with equal possibly infinite defect numbers in a Hilbert space in terms of Nevanlinna families in a parameter space. The aim of this note is to give a simple complete analytical proof of Krein's formula. (c) 2008 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	567-578
Number of pages	12
Journal	Journal of Mathematical Analysis and Applications
Volume	351
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2008.10.046
Publication status	Published - 15-Mar-2009

Keywords

Krein's formula
Krein-Naimark formula
Generalized resolvent
Symmetric operator
Selfadjoint extension
Boundary triplet
GENERALIZED RESOLVENTS
HILBERT-SPACE
OPERATORS

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title = "On Krein's formula",

abstract = "Krein's formula provides a parametrization of the generalized resolvents and Straus extensions of a closed symmetric operator with equal possibly infinite defect numbers in a Hilbert space in terms of Nevanlinna families in a parameter space. The aim of this note is to give a simple complete analytical proof of Krein's formula. (c) 2008 Elsevier Inc. All rights reserved.",

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author = "Jussi Behrndt and {de Snoo}, Henk",

year = "2009",

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day = "15",

doi = "10.1016/j.jmaa.2008.10.046",

language = "English",

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journal = "Journal of Mathematical Analysis and Applications",

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AU - Behrndt, Jussi

AU - de Snoo, Henk

PY - 2009/3/15

Y1 - 2009/3/15

N2 - Krein's formula provides a parametrization of the generalized resolvents and Straus extensions of a closed symmetric operator with equal possibly infinite defect numbers in a Hilbert space in terms of Nevanlinna families in a parameter space. The aim of this note is to give a simple complete analytical proof of Krein's formula. (c) 2008 Elsevier Inc. All rights reserved.

AB - Krein's formula provides a parametrization of the generalized resolvents and Straus extensions of a closed symmetric operator with equal possibly infinite defect numbers in a Hilbert space in terms of Nevanlinna families in a parameter space. The aim of this note is to give a simple complete analytical proof of Krein's formula. (c) 2008 Elsevier Inc. All rights reserved.

KW - Krein's formula

KW - Krein-Naimark formula

KW - Generalized resolvent

KW - Symmetric operator

KW - Selfadjoint extension

KW - Boundary triplet

KW - GENERALIZED RESOLVENTS

KW - HILBERT-SPACE

KW - OPERATORS

U2 - 10.1016/j.jmaa.2008.10.046

DO - 10.1016/j.jmaa.2008.10.046

M3 - Article

SN - 0022-247X

VL - 351

SP - 567

EP - 578

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

On Krein's formula

Abstract

Keywords

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