On a generalization of Smirnov's theorem with some applications

Lasha Ephremidze, Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    We present a certain generalization of Smirnov's theorem on functions from the Hardy spaces H p Hp . We provide some applications of the proposed generalization. Namely, we give an equivalent characterization of outer analytic rectangular matrix functions, and give a simple proof of the uniqueness of spectral factorization of rank deficient matrices.

    Original languageEnglish (US)
    Pages (from-to)217-220
    Number of pages4
    JournalGeorgian Mathematical Journal
    Volume25
    Issue number2
    DOIs
    StatePublished - Jun 1 2018

    Fingerprint

    Spectral Factorization
    Matrix Function
    Hardy Space
    Theorem
    Uniqueness
    Generalization

    Keywords

    • matrix spectral factorization
    • outer matrix functions
    • Smirnov's theorem

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    On a generalization of Smirnov's theorem with some applications. / Ephremidze, Lasha; Spitkovsky, Ilya.

    In: Georgian Mathematical Journal, Vol. 25, No. 2, 01.06.2018, p. 217-220.

    Research output: Contribution to journalArticle

    Ephremidze, Lasha ; Spitkovsky, Ilya. / On a generalization of Smirnov's theorem with some applications. In: Georgian Mathematical Journal. 2018 ; Vol. 25, No. 2. pp. 217-220.
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