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Spectral analysis of the diffusion operator with random jumps from the boundary

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    SYSNO ASEP0466585
    Document TypeJ - Journal Article
    R&D Document TypeJournal Article
    Subsidiary JČlánek ve WOS
    TitleSpectral analysis of the diffusion operator with random jumps from the boundary
    Author(s) Kolb, M. (DE)
    Krejčiřík, David (UJF-V) RID
    Number of authors2
    Source TitleMathematische Zeitschrift - ISSN 0025-5874
    Roč. 284, 3-4 (2016), s. 877-900
    Number of pages24 s.
    Publication formPrint - P
    Languageeng - English
    CountryDE - Germany
    Keywordsself-adjoint operators ; eigenvalues ; eigenfunctions
    Subject RIVBE - Theoretical Physics
    R&D ProjectsGA14-06818S GA ČR - Czech Science Foundation (CSF)
    Institutional supportUJF-V - RVO:61389005
    UT WOS000386769300008
    EID SCOPUS84968616677
    DOI10.1007/s00209-016-1677-y
    AnnotationUsing an operator-theoretic framework in a Hilbert-space setting, we perform a detailed spectral analysis of the one-dimensional Laplacian in a bounded interval, subject to specific non-self-adjoint connected boundary conditions modelling a random jump from the boundary to a point inside the interval. In accordance with previous works, we find that all the eigenvalues are real. As the new results, we derive and analyse the adjoint operator, determine the geometric and algebraic multiplicities of the eigenvalues, write down formulae for the eigenfunctions together with the generalised eigenfunctions and study their basis properties. It turns out that the latter heavily depend on whether the distance of the interior point to the centre of the interval divided by the length of the interval is rational or irrational. Finally, we find a closed formula for the metric operator that provides a similarity transform of the problem to a self-adjoint operator.
    WorkplaceNuclear Physics Institute
    ContactMarkéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 ; Renata Glasová, glasova@ujf.cas.cz, Tel.: 266 177 223
    Year of Publishing2017
Number of the records: 1