Geodesic
On approximate solution of certain equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 9-17

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In this paper, we consider problems of discrete approximation of special integral operators with the Calderon–Zygmund kernel. We introduce discrete spaces and discrete operators acting in these spaces that are used proposed for for the approximate solution of the corresponding equations. We propose theorems on the solvability of equations with discrete operators, compare integral operators with their discrete analogs, and obtain estimates of errors of approximate solutions.
Keywords: Calderon–Zygmund kernel, discrete operator, approximation measure, approximate solution.
Mots-clés : symbol 
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     title = {On approximate solution of certain equations},
     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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A. V. Vasil'ev. On approximate solution of certain equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 9-17. http://geodesic.mathdoc.fr/item/INTO_2019_160_a1/