Factorization of some triangular matrix functions and its applications

Yu I. Karlovich, J. Loreto-Hernández, Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    We consider defined on the real line ℝ matrix functions with monomial terms of the form ceiλx on the main diagonal and one row, and with zero entries elsewhere. The factorability of such matrices is established and, moreover, the algorithm for their factorization is provided. In particular, formulas for the partial indices are derived, and conditions for them to all equal zero (that is, for the factorization to be canonical) are stated. These results are then used to obtain Fredholmness criteria for some convolution type equations on unions of intervals.

    Original languageEnglish (US)
    Pages (from-to)1-29
    Number of pages29
    JournalOperators and Matrices
    Volume9
    Issue number1
    DOIs
    StatePublished - Jan 1 2015

    Fingerprint

    Triangular matrix
    Matrix Function
    Factorization
    Fredholmness
    Zero
    Monomial
    Real Line
    Convolution
    Union
    Partial
    Interval
    Term
    Form

    Keywords

    • Almost periodic factorization
    • Convolution type equations
    • Fredholm operators
    • Geometric mean

    ASJC Scopus subject areas

    • Analysis
    • Algebra and Number Theory

    Cite this

    Factorization of some triangular matrix functions and its applications. / Karlovich, Yu I.; Loreto-Hernández, J.; Spitkovsky, Ilya.

    In: Operators and Matrices, Vol. 9, No. 1, 01.01.2015, p. 1-29.

    Research output: Contribution to journalArticle

    Karlovich, YI, Loreto-Hernández, J & Spitkovsky, I 2015, 'Factorization of some triangular matrix functions and its applications', Operators and Matrices, vol. 9, no. 1, pp. 1-29. https://doi.org/10.7153/oam-09-01
    Karlovich, Yu I. ; Loreto-Hernández, J. ; Spitkovsky, Ilya. / Factorization of some triangular matrix functions and its applications. In: Operators and Matrices. 2015 ; Vol. 9, No. 1. pp. 1-29.
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