V. V. Andrievskii, “The geometric structure of regions, and direct theorems of the constructive theory of functions”, Math. USSR-Sb., 54:1 (1986), 39

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Mathematics of the USSR-Sbornik, 1986, Volume 54, Issue 1, Pages 39–56
DOI: https://doi.org/10.1070/SM1986v054n01ABEH002959 (Mi sm1823)

This article is cited in 17 scientific papers (total in 17 papers)

The geometric structure of regions, and direct theorems of the constructive theory of functions

V. V. Andrievskii

English version PDF (860 kB) Citations (17) Russian version article

References:

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DOI: https://doi.org/10.1070/SM1986v054n01ABEH002959

Abstract: Sufficient conditions and necessary conditions close to them are obtained for a bounded domain $G$ with Jordan boundary $L=\partial G$ to admit direct theorems of approximation theory in terms of the distance $\rho_{1+\frac1n}(z)$ from boundary points $z\in L$ to the $\bigl(1+\frac1n\bigr)$th level line of the function that maps the complement of the domain on the exterior of the unit disk.
Bibliography: 21 titles.

Received: 15.03.1984

Bibliographic databases:

UDC: 517.53

MSC: 30E10

Language: English

Original paper language: Russian

Citation: 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

Citation in format AMSBIB

\Bibitem{And85}

\by V.~V.~Andrievskii

\paper The geometric structure of regions, and direct theorems of the constructive theory of functions

\jour Math. USSR-Sb.

\yr 1986

\vol 54

\issue 1

\pages 39--56

\mathnet{http://mi.mathnet.ru/eng/sm1823}

\crossref{https://doi.org/10.1070/SM1986v054n01ABEH002959}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=773428}

\zmath{https://zbmath.org/?q=an:0584.30033|0578.30030}

Linking options:

https://www.mathnet.ru/eng/sm1823

https://doi.org/10.1070/SM1986v054n01ABEH002959

https://www.mathnet.ru/eng/sm/v168/i1/p41

This publication is cited in the following 17 articles:

T. A. Alekseeva, N. A. Shirokov, “Hölder classes in the $L^p$ norm on a chord-arc curve in $\mathbb R^3$”, St. Petersburg Math. J., 34:4 (2023), 557–571
D. A. Pavlov, “Constructive Description of Hölder Classes on Compact Subsets of ℝ3”, J Math Sci, 261:6 (2022), 808
D. A. Pavlov, “Constructive description of Hölder classes on some multidimensional compact sets”, Vestn. St. Petersbg. Univ., Math., 8:4 (2021), 245–253
D. A. Pavlov, “Konstruktivnoe opisanie gëlderovykh klassov na kompaktakh v $\mathbb{R}^3$”, Issledovaniya po lineinym operatoram i teorii funktsii. 48, Zap. nauchn. sem. POMI, 491, POMI, SPb., 2020, 119–144
Tatyana A. Alexeeva, Nikolay A. Shirokov, “Constructive description of Hölder-like classes on an arc in R3 by means of harmonic functions”, Journal of Approximation Theory, 249 (2020), 105308
Vladimir Andrievskii, “Weighted uniform polynomial approximation and moduli of smoothness on continua in the complex plane”, Journal of Approximation Theory, 2011
Vladimir Andrievskii, Hans-Peter Blatt, “On approximation of continuous functions by trigonometric polynomials”, Journal of Approximation Theory, 163:2 (2011), 249
Jafarov S.Z., “Approximation of Functions by Rational Functions on Closed Curves of the Complex Plane”, Arab. J. Sci. Eng., 36:8 (2011), 1529–1534
V. V. Andrievskii, “On Approximation of Continuous Functions by Entire Functions on Subsets of the Real Line”, Constr Approx, 2009
Andrievskii V., “Polynomial Approximation of Analytic Functions on a Finite Number of Continua in the Complex Plane”, J. Approx. Theory, 133:2 (2005), 238–244
V.V. Andrievskii, Handbook of Complex Analysis, 1, Geometric Function Theory, 2002, 493
Vladimir V Andrievskii, Igor E Pritsker, Richard S Varga, “Simultaneous approximation and interpolation of functions on continua in the complex plane”, Journal de Mathématiques Pures et Appliquées, 80:4 (2001), 373
Shirokov N., “Dzyadyk,V.K. Approximation on Compacts with Infinite-Connected Completion”, Dokl. Akad. Nauk, 335:6 (1994), 700–701
V. V. Andrievskii, V. I. Belyi, V. V. Maimeskul, “Approximation of solutions of the equation $\overline\partial^jf=0$, $j\geqslant1$, in domain with quasiconformal boundary”, Math. USSR-Sb., 68:2 (1991), 303–323
E. A. Andrievskii, “Measurement of magnetic parameters and calibration of permanent magnets in apparatus with an incompletely closed magnetic system”, Meas Tech, 32:9 (1989), 898
J. M. Anderson, A. Hinkkanen, F. D. Lesley, “On theorems of Jackson and Bernstein type in the complex plane”, Constr Approx, 4:1 (1988), 307
Dieter Gaier, “On the convergence of the Bieberbach polynomials in regions with corners”, Constr Approx, 4:1 (1988), 289

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