Integral operators of the L-convolution type in the case of a reflectionless potential

Davresh Hasanyan, Armen Kamalyan, Martin Karakhanyan, Ilya M. Spitkovsky

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The notion of the L-convolution operator is introduced by changing the Fourier operator in the definition of the (regular) convolution operator to the operator intertwining the Sturm-Liouville operator L with the multiplication operator. Along the same lines, the L-Wiener-Hopf operator is introduced. For the latter, the invertibility is studied in the case of a reflectionless potential and piecewise continuous symbols.

Original languageEnglish (US)
Title of host publicationModern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Revised and Extended Contributions
EditorsAlexey Karapetyants, Vladislav Kravchenko, Elijah Liflyand
PublisherSpringer New York LLC
Pages175-197
Number of pages23
ISBN (Print)9783030267476
DOIs
StatePublished - 2019
EventInternational Scientific Conference of Modern Methods and Problems of Operator Theory and Harmonic Analysis and Their Applications, OTHA 2018 - Rostov-on-Don, Russian Federation
Duration: Apr 22 2018Apr 27 2018

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume291
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Scientific Conference of Modern Methods and Problems of Operator Theory and Harmonic Analysis and Their Applications, OTHA 2018
CountryRussian Federation
CityRostov-on-Don
Period4/22/184/27/18

Keywords

  • L-Symbol
  • L-Wiener-Hopf operator
  • Reflectionless potential

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Hasanyan, D., Kamalyan, A., Karakhanyan, M., & Spitkovsky, I. M. (2019). Integral operators of the L-convolution type in the case of a reflectionless potential. In A. Karapetyants, V. Kravchenko, & E. Liflyand (Eds.), Modern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Revised and Extended Contributions (pp. 175-197). (Springer Proceedings in Mathematics and Statistics; Vol. 291). Springer New York LLC. https://doi.org/10.1007/978-3-030-26748-3_11