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This article is cited in 8 scientific papers (total in 8 papers)
A criterion for uniform approximability of individual functions by solutions of second-order homogeneous elliptic equations with constant complex coefficients
M. Ya. Mazalovab a National Research University "Moscow Power Engineering Institute", Smolensk, Russia
b Saint Petersburg State University, St. Petersburg, Russia
Abstract:
A natural counterpart of Vitushkin's criterion is obtained in the problem of uniform approximation of functions by solutions of second-order homogeneous elliptic equations with constant complex coefficient on compact subsets of $\mathbb R^d$, $d\geqslant3$. It is stated in terms of a single (scalar) capacity connected with the leading coefficient of the Laurent series. The scheme of approximation uses methods in the theory of singular integrals and, in particular, constructions of certain special Lipschitz surfaces and Carleson measures.
Bibliography: 23 titles.
Keywords:
uniform approximation, capacities, singular integrals, Carleson measures, Vitushkin's scheme.
Received: 06.06.2019 and 05.06.2020
Citation:
M. Ya. Mazalov, “A criterion for uniform approximability of individual functions by solutions of second-order homogeneous elliptic equations with constant complex coefficients”, Sb. Math., 211:9 (2020), 1267–1309
Linking options:
https://www.mathnet.ru/eng/sm9288https://doi.org/10.1070/SM9288 https://www.mathnet.ru/eng/sm/v211/i9/p60
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Abstract page: | 354 | Russian version PDF: | 49 | English version PDF: | 27 | References: | 40 | First page: | 6 |
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