Two-dimensional trace-normed canonical systems of differential equations and selfadjoint interface conditions

H de Snoo*, Henrik Winkler

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    2 Citations (Scopus)
    9 Downloads (Pure)

    Abstract

    The class of two-dimensional trace-normed canonical systems of differential equations on R is considered with selfadjoint interface conditions at 0. If one or both of the intervals around 0 are H-indivisible the interface conditions which give rise to selfadjoint relations (multi-valued operators) are determined. It is shown that the corresponding generalized Fourier transforms are partially isometric. Compression to the halfline (0,∞) results in boundary conditions which depend on the eigenvalue parameter involving a fractional linear transform of the Titchmarsh-Weyl coefficient of the halfline (−∞, 0). The corresponding generalized Fourier transforms are isometric except possibly on a one-dimensional subspace where they are contractive.
    Original languageEnglish
    Pages (from-to)73-108
    Number of pages36
    JournalIntegral equations and operator theory
    Volume51
    Issue number1
    DOIs
    Publication statusPublished - Jan-2005

    Keywords

    • canonical system
    • Titchmarsh-Weyl coefficient
    • Q-function
    • Nevanlinna function
    • interface condition
    • Fourier transform
    • spectral matrix
    • multiplicity
    • INNER MATRIX FUNCTIONS
    • INVERSE MONODROMY PROBLEM
    • SPECTRAL FUNCTIONS
    • LINEAR RELATION
    • INTERPOLATION

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