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On a Riemann Boundary Value Problem with Infinite Index in the Half-plane

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Operator Theory and Harmonic Analysis (OTHA 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 357))

Abstract

The paper considers the Riemann boundary value problem in the half-plane in the space L 1(ρ). The weight function ρ(x) has infinite number of zeros on the real axis. The boundary condition is understood in the sense of L 1(ρ). A necessary and sufficient condition is obtained for the normal solvability of the considered problem. The solutions are represented in explicit form.

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Acknowledgements

Smbat Aghekyan is supported by Russian Foundation for Fundamental Research (project number 19-31-50043).

Author information

Authors and Affiliations

  1. Yerevan State University, Yerevan, Armenia

    Hrachik M. Hayrapetyan & Artavazd D. Ohanyan

  2. Yerevan State University, Yerevan, Armenia

    Smbat A. Aghekyan

  3. Regional Mathematical Center of Southern Federal University, Rostov-on-Don, Russia

    Smbat A. Aghekyan

Authors
  1. Hrachik M. Hayrapetyan
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  2. Smbat A. Aghekyan
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  3. Artavazd D. Ohanyan
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, Mechanic and Computer Sciences and Regional Mathematical Center, Southern Federal University, Rostov-on-Don, Russia

    Alexey N. Karapetyants

  2. Department of Mathematics, Cinvestav, Santiago de Queretaro, Querétaro, Mexico

    Vladislav V. Kravchenko

  3. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    Elijah Liflyand

  4. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Helmuth R. Malonek

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Hayrapetyan, H.M., Aghekyan, S.A., Ohanyan, A.D. (2021). On a Riemann Boundary Value Problem with Infinite Index in the Half-plane. In: Karapetyants, A.N., Kravchenko, V.V., Liflyand, E., Malonek, H.R. (eds) Operator Theory and Harmonic Analysis. OTHA 2020. Springer Proceedings in Mathematics & Statistics, vol 357. Springer, Cham. https://doi.org/10.1007/978-3-030-77493-6_13

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