Toeplitz operators of finite interval type and the table method

M. C. Câmara, C. Diogo, Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    We solve a Riemann-Hilbert problem with almost periodic coefficient G, associated to a Toeplitz operator TG in a class which is closely connected to finite interval convolution equations, based on a generalization of the so-called table method. The explicit determination of solutions to that problem allows one to establish necessary and sufficient conditions for the invertibility of the corresponding Toeplitz operator, and to determine an appropriate factorization of G, providing explicit formulas for the inverse of TG. Some unexpected properties of the Fourier spectrum of the solutions are revealed which are not apparent through other approaches to the same problem.

    Original languageEnglish (US)
    Pages (from-to)1148-1173
    Number of pages26
    JournalJournal of Mathematical Analysis and Applications
    Volume432
    Issue number2
    DOIs
    StatePublished - Jan 1 2015

    Fingerprint

    Toeplitz Operator
    Factorization
    Convolution
    Mathematical operators
    Table
    Convolution Equation
    Fourier Spectrum
    Interval
    Riemann-Hilbert Problem
    Periodic Coefficients
    Invertibility
    Almost Periodic
    Explicit Formula
    Necessary Conditions
    Sufficient Conditions
    Class
    Generalization

    Keywords

    • Almost periodic function
    • Factorization theory
    • Riemann-Hilbert problem
    • Toeplitz operator

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Toeplitz operators of finite interval type and the table method. / Câmara, M. C.; Diogo, C.; Spitkovsky, Ilya.

    In: Journal of Mathematical Analysis and Applications, Vol. 432, No. 2, 01.01.2015, p. 1148-1173.

    Research output: Contribution to journalArticle

    Câmara, M. C. ; Diogo, C. ; Spitkovsky, Ilya. / Toeplitz operators of finite interval type and the table method. In: Journal of Mathematical Analysis and Applications. 2015 ; Vol. 432, No. 2. pp. 1148-1173.
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