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 Mat. Sb. (N.S.), 1984, Volume 125(167), Number 1(9), Pages 70–87 (Mi msb2072)

Approximation characterization of classes of functions on continua of the complex plane

V. V. Andrievskii

Abstract: One possible method is suggested for the constructive description of function classes defined on continua of the complex plane for which the traditional (in this subject area) description in terms of distances from boundary points to corresponding level curves of the outer Riemann function generally does not exist.
The main idea of the constructions and results presented consists in taking account of the growth of derivatives of polynomials approximating the function.
Bibliography: 28 titles.

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English version:
Mathematics of the USSR-Sbornik, 1986, 53:1, 69–87

Bibliographic databases:

UDC: 517.53
MSC: 30E10

Citation: V. V. Andrievskii, “Approximation characterization of classes of functions on continua of the complex plane”, Mat. Sb. (N.S.), 125(167):1(9) (1984), 70–87; Math. USSR-Sb., 53:1 (1986), 69–87

Citation in format AMSBIB
\Bibitem{And84} \by V.~V.~Andrievskii \paper Approximation characterization of classes of functions on continua of the complex plane \jour Mat. Sb. (N.S.) \yr 1984 \vol 125(167) \issue 1(9) \pages 70--87 \mathnet{http://mi.mathnet.ru/msb2072} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=760414} \zmath{https://zbmath.org/?q=an:0606.30036} \transl \jour Math. USSR-Sb. \yr 1986 \vol 53 \issue 1 \pages 69--87 \crossref{https://doi.org/10.1070/SM1986v053n01ABEH002910} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. V. Andrievskii, “On approximation of functions by harmonic polynomials”, Math. USSR-Izv., 30:1 (1988), 1–13
2. 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
3. V. V. Andrievskii, V. V. Maimeskul, “Constructive description of certain classes of functions on quasismooth arcs”, Russian Acad. Sci. Izv. Math., 44:1 (1995), 193–206
4. Leonhard Frerick, Jürgen Müller, “Polynomial Approximation on Compact Sets Bounded by Dini-Smooth Arcs”, Comput. Methods Funct. Theory, 3:1 (2004), 273
5. Vladimir V. Andrievskii, Hans-Peter Blatt, “Polynomial Approximation of Functions on a Quasi-Smooth Arc with Hermitian Interpolation”, Constr Approx, 2009
6. 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
7. Vladimir Andrievskii, “Approximation of Functions by Reciprocals of Polynomials on a Quasi-Smooth Arc”, SIAM J. Math. Anal, 44:4 (2012), 2329
8. Jafarov S.Z., “Approximation of Conjugate Functions by Trigonometric Polynomials in Weighted Orlicz Spaces”, J. Math. Inequal., 7:2 (2013), 271–281
9. Vladimir Andrievskii, “Polynomial approximation of polyharmonic functions on a complement of a John Domain”, Journal of Approximation Theory, 2014
10. T. A. Alexeeva, N. A. Shirokov, “Constructive description of function classes on surfaces in $\mathbb{R}^3$ and $\mathbb{R}^4$”, Probl. anal. Issues Anal., 8(26):3 (2019), 16–23
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