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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    9 Citations (Scopus)
    319 Downloads (Pure)

    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 languageEnglish
    Pages (from-to)1087-1117
    Number of pages31
    JournalIndagationes mathematicae-New series
    Volume23
    Issue number4
    DOIs
    Publication statusPublished - 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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