Singular Sturm-Liouville problems whose coefficients depend rationally on the eigenvalue parameter

Seppo Hassi, M Moller*, H de Snoo

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    8 Citations (Scopus)


    Let -Domega((.), z)D + q be a differential operator in L-2(0, infinity) whose leading coefficient contains the eigenvalue parameter z. For the case that omega((.), z) has the particular form

    omega(t, z) = p(t) + c(t)(2)/(z - r (t)), z is an element of C \ R,

    and the coefficient functions satisfy certain local integrability conditions, it is shown that there is an analog for the usual limit-point/limit-circle classification. In the limit-point case mild sufficient conditions are given so that all but one of the Titchmarsh-Weyl coefficients belong to the so-called Kac subclass of Nevanlinna functions. An interpretation of the Titchmarsh-Weyl coefficients is given also in terms of an associated system of differential equations where the eigenvalue parameter appears linearly. (C) 2004 Elsevier Inc. All rights reserved.

    Original languageEnglish
    Pages (from-to)258-275
    Number of pages18
    JournalJournal of Mathematical Analysis and Applications
    Issue number1
    Publication statusPublished - 1-Jul-2004


    • floating singularity
    • Sturm-Liouville operator
    • Titchmarsh-Weyl coefficient
    • limit-point/limit-circle
    • Kac class
    • symmetric operator
    • self-adjoint extension


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