Asymptotic Expansions of Generalized Nevanlinna Functions and their Spectral Properties

Vladimir Derkach, Seppo Hassi, Hendrik de Snoo

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

    8 Citations (Scopus)
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    Abstract

    Asymptotic expansions of generalized Nevanlinna functions Q are investigated by means of a factorization model involving a part of the generalized zeros and poles of nonpositive type of the function Q. The main results in this paper arise from the explicit construction of maximal Jordan chains in the root subspace R∞(SF) of the so-called generalized Friedrichs extension. A classification of maximal Jordan chains is introduced and studied in analytical terms by establishing the connections to the appropriate asymptotic expansions. This approach results in various new analytic characterizations of the spectral properties of selfadjoint relations in Pontryagin spaces and, conversely, translates analytic and asymptotic properties of generalized Nevanlinna functions into the spectral theoretical properties of self-adjoint relations in Pontryagin spaces.
    Original languageEnglish
    Title of host publicationOperator Theory in Inner Product Spaces
    PublisherBirkhauser
    Pages51-88
    Number of pages38
    Volume175
    ISBN (Electronic)978-3-7643-8270-4
    ISBN (Print)978-3-7643-8269-8
    DOIs
    Publication statusPublished - 2007

    Publication series

    NameOperator Theory: Advances and Applications

    Keywords

    • generalized Friedrichs extension
    • factorization
    • operator model
    • selfadjoint extension
    • Pontryagin space
    • symmetric operator
    • asymptotic expansion
    • generalized Nevanlinna function

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