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

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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

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