Geodesic
On a discrete equation in a quarter-plane and a related boundary-value problem
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 1, Tome 206 (2022), pp. 15-22

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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, periodic wave factorization, analyticity, solvability.
Mots-clés : pair equation 
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     title = {On a discrete equation in a quarter-plane and a related boundary-value problem},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
     volume = {206},
     year = {2022},
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V. B. Vasilev (Vasilyev); A. A. Khodyreva. On a discrete equation in a quarter-plane and a related boundary-value problem. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 1, Tome 206 (2022), pp. 15-22. http://geodesic.mathdoc.fr/item/INTO_2022_206_a1/