### 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 language | English (US) |
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Title of host publication | Modern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Revised and Extended Contributions |

Editors | Alexey Karapetyants, Vladislav Kravchenko, Elijah Liflyand |

Publisher | Springer New York LLC |

Pages | 175-197 |

Number of pages | 23 |

ISBN (Print) | 9783030267476 |

DOIs | |

State | Published - 2019 |

Event | International 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 2018 → Apr 27 2018 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 291 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | International Scientific Conference of Modern Methods and Problems of Operator Theory and Harmonic Analysis and Their Applications, OTHA 2018 |
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Country | Russian Federation |

City | Rostov-on-Don |

Period | 4/22/18 → 4/27/18 |

### 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