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Spectral analysis of the diffusion operator with random jumps from the boundary
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SYSNO ASEP 0466585 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Spectral analysis of the diffusion operator with random jumps from the boundary Author(s) Kolb, M. (DE)
Krejčiřík, David (UJF-V) RIDNumber of authors 2 Source Title Mathematische Zeitschrift. - : Springer - ISSN 0025-5874
Roč. 284, 3-4 (2016), s. 877-900Number of pages 24 s. Publication form Print - P Language eng - English Country DE - Germany Keywords self-adjoint operators ; eigenvalues ; eigenfunctions Subject RIV BE - Theoretical Physics R&D Projects GA14-06818S GA ČR - Czech Science Foundation (CSF) Institutional support UJF-V - RVO:61389005 UT WOS 000386769300008 EID SCOPUS 84968616677 DOI 10.1007/s00209-016-1677-y Annotation Using 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2017
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