Abstract:
This paper is devoted to an application of the methods of geometric function theory of a single complex variable and some results from the theory of conformal and quasiconformal mappings to a solution of the direct problem of the constructive theory of functions.
Direct theorems are obtained for the theory of approximation of functions regular in regions bounded by quasiconformal curves admitting a geometric description. In particular, direct theorems are obtained for arbitrary bounded convex regions.
Citation:
V. I. Belyi, V. M. Miklyukov, “Some properties of conformal and quasiconformal mappings and direct theorems of the constructive theory of functions”, Math. USSR-Izv., 8:6 (1974), 1323–1341
\Bibitem{BelMik74}
\by V.~I.~Belyi, V.~M.~Miklyukov
\paper Some properties of conformal and quasiconformal mappings and direct theorems of the constructive theory of functions
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 6
\pages 1323--1341
\mathnet{http://mi.mathnet.ru/eng/im2015}
\crossref{https://doi.org/10.1070/IM1974v008n06ABEH002150}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=387603}
\zmath{https://zbmath.org/?q=an:0312.30035}
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https://www.mathnet.ru/eng/im2015
https://doi.org/10.1070/IM1974v008n06ABEH002150
https://www.mathnet.ru/eng/im/v38/i6/p1343
This publication is cited in the following 7 articles:
K. A. Sintsova, N. A. Shirokov, “Approximation by Double Periodic Functions in the Classes Cr∗A”, Vestnik St.Petersb. Univ.Math., 57:3 (2024), 345
K. А. Sintsova, N. A. Shirokov, “Approximation by polynomials composed of Weierstrass doubly periodic functions”, Vestn. St. Petersbg. Univ., Math., 56:1 (2023), 46–56
Vladimir Andrievskii, “On the Approximation of a Continuum by Lemniscates”, Journal of Approximation Theory, 105:2 (2000), 292
V. V. Andrievskii, “A constructive characterization of harmonic functions in domains with quasiconformal boundaries”, Math. USSR-Izv., 34:2 (1990), 441–454
V. V. Andrievskii, “On approximation of functions by harmonic polynomials”, Math. USSR-Izv., 30:1 (1988), 1–13
V. V. Andrievskii, “The geometric structure of regions, and direct theorems of the constructive theory of functions”, Math. USSR-Sb., 54:1 (1986), 39–56
V. I. Belyi, “Conformal mappings and the approximation of analytic functions in domains with a quasiconformal boundary”, Math. USSR-Sb., 31:3 (1977), 289–317
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