On Exceptional Extensions Close to the Generalized Friedrichs Extension of Symmetric Operators

Seppo Hassi, Henk de Snoo, Henrik Winkler

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

    2 Citations (Scopus)
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    Abstract

    If the Q-function Q corresponding to a closed symmetric operator S with defect numbers (1, 1) and one of its selfadjoint extensions belongs to the Kac class N1 then it is known that all except one of the Q-functions of S belong to N1, too. In this note the situation that the given Q-function does not belong to the class N1 is considered. If Q ∈ Np, i.e., if the restriction of the spectral measure of Q on the positive or the negative axis corresponds to an N1-function, then Q itself is the Q-function of the exceptional extension, and, hence, it is associated with the generalized Friedrichs extension of S. If Q or, equivalently, the spectral measure of Q is symmetric, or if the difference of Q and a symmetric Nevanlinna function belongs to the class N1 or Np, then Q is still exceptional in a wider sense. Similar results hold for the generalized Kreĭn-von Neumann extension of the symmetric operator.
    Original languageEnglish
    Title of host publicationOperator Theory in Inner Product Spaces
    PublisherBirkhauser
    Pages111-12-
    Number of pages10
    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

    • Kac class
    • generalized Kreĭn-von Neumann extension
    • generalized Friedrichs extension
    • Q-function

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