Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 206, Pages 15–22
DOI: https://doi.org/10.36535/0233-6723-2022-206-15-22 (Mi into961) 		 
On a discrete equation in a quarter-plane and a related boundary-value problem

V. B. Vasilev (Vasilyev), A. A. Khodyreva

National Research University "Belgorod State University"
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DOI: https://doi.org/10.36535/0233-6723-2022-206-15-22
Abstract: Discrete equations of the convolution type in a quarter-plane are considered. We prove that each such equation is equivalent to an analog of the two-dimensional periodic Riemann problem on the torus. We describe sufficient conditions for the unique solvability of such a periodic Riemann problem and, as a consequence, conditions for the unique solvability of a discrete equation in terms of the symbol of the convolution operator.
Keywords: discrete pseudodifferential operator, two-dimensional periodic Riemann problem, pair equation, periodic wave factorization, analyticity, solvability.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation FZWG-2020-0029
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (project No. FZWG-2020-0029).
Document Type: Article
UDC: 517.954, 517.983
MSC: 35S15, 47B38
Language: Russian
Citation: V. B. Vasilev (Vasilyev), A. A. Khodyreva, “On a discrete equation in a quarter-plane and a related boundary-value problem”, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 206, VINITI, Moscow, 2022, 15–22
Citation in format AMSBIB
\Bibitem{VasKho22}
\by V.~B.~Vasilev~(Vasilyev), A.~A.~Khodyreva
\paper On a discrete equation in a quarter-plane and a related boundary-value problem
\inbook Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 206
\pages 15--22
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into961}
\crossref{https://doi.org/10.36535/0233-6723-2022-206-15-22}
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