Spectral properties of birth-death polynomials

Erik A. van Doorn

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    Abstract

    We consider sequences of polynomials that are defined by a three-terms recurrence relation and orthogonal with respect to a positive measure on the nonnegative axis. By a famous result of Karlin and McGregor such sequences are instrumental in the analysis of birth-death processes. Inspired by problems and results in this stochastic setting we present necessary and sufficient conditions in terms of the parameters in the recurrence relation for the smallest or second smallest point in the support of the orthogonalizing measure to be larger than zero, and for the support to be discrete with no finite limit point.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages17
    Publication statusPublished - Mar 2014

    Publication series

    NameMemorandum
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.2035
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • Stieltjes moment problem
    • Spectrum
    • Birth-death process
    • METIS-304050
    • IR-90385
    • EWI-24642
    • Orthogonal polynomials
    • Orthogonalizing measure

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