Generalized Friedrichs Extensions Associated with Interface Conditions for Sturm-Liouville Operators

Andreas Fleige, Seppo Hassi, Henk de Snoo, Henrik Winkler

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    Abstract

    For a class of Sturm-Liouville operators with an interface condition at an interior point all selfadjoint realizations are determined. This result is obtained via a description of the selfadjoint extensions of the coupling of two symmetric operators. The (generalized) Friedrichs extension, when it exists, is determined. Sufficient conditions for the (generalized) Friedrichs extension to exist are given.
    Original languageEnglish
    Title of host publicationOperator Theory and Indefinite Inner Product Spaces
    PublisherBirkhauser
    Pages135-145
    Number of pages11
    Volume163
    ISBN (Electronic)978-3-7643-7516-4
    ISBN (Print)978-3-7643-7515-7
    DOIs
    Publication statusPublished - 2005

    Publication series

    NameOperator Theory: Advances and Applications

    Keywords

    • interface condition
    • Weyl function
    • boundary triplet
    • (generalized) Friedrichs extension
    • selfadjoint extension
    • symmetric operator

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