Zeros of nonpositive type of generalized Nevanlinna functions with one negative square

Henk de Snoo, Henrik Winkler, Michal Wojtylak*

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    7 Citations (Scopus)
    10 Downloads (Pure)

    Abstract

    A generalized Nevanlinna function Q(z) with one negative square has precisely one generalized zero of nonpositive type in the closed extended upper halfplane. The fractional linear transformation defined by Qτ(z) = (Q(z) − τ )/(1 + τQ(z)), τ ∈ R ∪ {∞}, is a generalized Nevanlinna function with one negative square. Its generalized zero of nonpositive type α(τ) as a function of τ defines a path in the closed upper halfplane. Various properties of this path are studied in detail.
    Original languageEnglish
    Pages (from-to)399-417
    Number of pages19
    JournalJournal of Mathematical Analysis and Applications
    Volume382
    Issue number1
    DOIs
    Publication statusPublished - 1-Oct-2011

    Keywords

    • Pontryagin space
    • Generalized Nevanlinna function
    • Generalized pole of nonpositive type
    • Generalized zero of nonpositive type
    • Integral representation
    • Fractional linear transformation
    • SELF-ADJOINT EXTENSIONS
    • LINEAR RELATION
    • KREIN SPACE
    • DEFECT ONE
    • OPERATORS
    • IIX

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