Spectral factorization of measurable rectangular matrix functions and the vector-valued Riemann problem

Marek Rakowski, Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    We define spectral factorization in Lp (or a generalized Wiener-Hopf factorization) of a measurable singular matrix function on a simple closed rectifiable contour Γ. Such factorization has the same uniqueness properties as in the nonsingular case. We discuss basic properties of the vector valued Riemann problem whose coefficient takes singular values almost everywhere on Γ. In particular, we introduce defect numbers for this problem which agree with the usual defect numbers in the case of a nonsingular coefficient. Based on the Riemann problem, we obtain a necessary and sufficient condition for existence of a spectral factorization in Lp.

    Original languageEnglish (US)
    Pages (from-to)669-696
    Number of pages28
    JournalRevista Matematica Iberoamericana
    Volume12
    Issue number3
    DOIs
    StatePublished - Jan 1 1996

    Fingerprint

    Spectral Factorization
    Matrix Function
    Cauchy Problem
    Defects
    Wiener-Hopf Factorization
    Singular Functions
    Singular matrix
    Coefficient
    Singular Values
    Factorization
    Uniqueness
    Necessary Conditions
    Closed
    Sufficient Conditions

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Spectral factorization of measurable rectangular matrix functions and the vector-valued Riemann problem. / Rakowski, Marek; Spitkovsky, Ilya.

    In: Revista Matematica Iberoamericana, Vol. 12, No. 3, 01.01.1996, p. 669-696.

    Research output: Contribution to journalArticle

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