Infinite-dimensional perturbations, maximally nondensely defined symmetric operators, and some matrix representations

S. Hassi; H.S.V. de Snoo; F.H. Szafraniec

doi:10.1016/j.indag.2012.08.007

Infinite-dimensional perturbations, maximally nondensely defined symmetric operators, and some matrix representations

S. Hassi, H.S.V. de Snoo, F.H. Szafraniec

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Abstract

The notion of a maximally nondensely defined symmetric operator or relation is introduced and characterized. The selfadjoint extensions (including the generalized Friedrichs extension) of a class of maximally nondensely defined symmetric operators are described. The description is given by means of the theory of ordinary boundary triplets and exhibits the extensions as infinite-dimensional perturbations of a certain selfadjoint operator extension of the symmetric operator. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	1087-1117
Number of pages	31
Journal	Indagationes mathematicae-New series
Volume	23
Issue number	4
DOIs	https://doi.org/10.1016/j.indag.2012.08.007
Publication status	Published - Dec-2012

Keywords

Symmetric operator
Generalized Friedrichs extension
Weyl function
Boundary triplet
Graph perturbation
SELF-ADJOINT RELATIONS
RANK-ONE PERTURBATIONS
SINGULAR PERTURBATIONS
EXTENSIONS

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title = "Infinite-dimensional perturbations, maximally nondensely defined symmetric operators, and some matrix representations",

abstract = "The notion of a maximally nondensely defined symmetric operator or relation is introduced and characterized. The selfadjoint extensions (including the generalized Friedrichs extension) of a class of maximally nondensely defined symmetric operators are described. The description is given by means of the theory of ordinary boundary triplets and exhibits the extensions as infinite-dimensional perturbations of a certain selfadjoint operator extension of the symmetric operator. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.",

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author = "S. Hassi and Snoo, \{H.S.V. de\} and F.H. Szafraniec",

note = "Relation: http://www.rug.nl/research/jbi/ Rights: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science",

year = "2012",

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doi = "10.1016/j.indag.2012.08.007",

language = "English",

volume = "23",

pages = "1087--1117",

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T1 - Infinite-dimensional perturbations, maximally nondensely defined symmetric operators, and some matrix representations

AU - Hassi, S.

AU - Snoo, H.S.V. de

AU - Szafraniec, F.H.

N1 - Relation: http://www.rug.nl/research/jbi/ Rights: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science

PY - 2012/12

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N2 - The notion of a maximally nondensely defined symmetric operator or relation is introduced and characterized. The selfadjoint extensions (including the generalized Friedrichs extension) of a class of maximally nondensely defined symmetric operators are described. The description is given by means of the theory of ordinary boundary triplets and exhibits the extensions as infinite-dimensional perturbations of a certain selfadjoint operator extension of the symmetric operator. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

AB - The notion of a maximally nondensely defined symmetric operator or relation is introduced and characterized. The selfadjoint extensions (including the generalized Friedrichs extension) of a class of maximally nondensely defined symmetric operators are described. The description is given by means of the theory of ordinary boundary triplets and exhibits the extensions as infinite-dimensional perturbations of a certain selfadjoint operator extension of the symmetric operator. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

KW - Symmetric operator

KW - Generalized Friedrichs extension

KW - Weyl function

KW - Boundary triplet

KW - Graph perturbation

KW - SELF-ADJOINT RELATIONS

KW - RANK-ONE PERTURBATIONS

KW - SINGULAR PERTURBATIONS

KW - EXTENSIONS

U2 - 10.1016/j.indag.2012.08.007

DO - 10.1016/j.indag.2012.08.007

M3 - Article

SN - 0019-3577

VL - 23

SP - 1087

EP - 1117

JO - Indagationes mathematicae-New series

JF - Indagationes mathematicae-New series

IS - 4

ER -

Infinite-dimensional perturbations, maximally nondensely defined symmetric operators, and some matrix representations

Abstract

Keywords

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