On the Fredholm Property of a Class of Convolution-Type Operators

A. G. Kamalyan, Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    The notions of the L-convolution operator and the ℒ-Wiener–Hopf operator are introduced by replacing the Fourier transform in the definition of the convolution operator by a spectral transformation of the self-adjoint Sturm–Liouville operator on the axis ℒ. In the case of the zero potential, the introduced operators coincide with the convolution operator and theWiener–Hopf integral operator, respectively. A connection between the ℒ-Wiener–Hopf operator and singular integral operators is revealed. In the case of a piecewise continuous symbol, a criterion for the Fredholm property and a formula for the index of the ℒ-Wiener–Hopf operator in terms of the symbol and the elements of the scattering matrix of the operator ℒ are obtained.

    Original languageEnglish (US)
    Pages (from-to)404-416
    Number of pages13
    JournalMathematical Notes
    Volume104
    Issue number3-4
    DOIs
    StatePublished - Sep 1 2018

    Fingerprint

    Fredholm Property
    Convolution
    Convolution Operator
    Operator
    Piecewise continuous
    Scattering Matrix
    Singular Integral Operator
    Integral Operator
    Class
    Fourier transform
    Zero

    Keywords

    • Fredholm property
    • singular integral operator
    • the operator L-Wiener–Hopf

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    On the Fredholm Property of a Class of Convolution-Type Operators. / Kamalyan, A. G.; Spitkovsky, Ilya.

    In: Mathematical Notes, Vol. 104, No. 3-4, 01.09.2018, p. 404-416.

    Research output: Contribution to journalArticle

    Kamalyan, A. G. ; Spitkovsky, Ilya. / On the Fredholm Property of a Class of Convolution-Type Operators. In: Mathematical Notes. 2018 ; Vol. 104, No. 3-4. pp. 404-416.
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