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.
Citation:
V. V. Andrievskii, “Approximation characterization of classes of functions on continua of the complex plane”, Math. USSR-Sb., 53:1 (1986), 69–87
\Bibitem{And84}
\by V.~V.~Andrievskii
\paper Approximation characterization of classes of functions on continua of the complex plane
\jour Math. USSR-Sb.
\yr 1986
\vol 53
\issue 1
\pages 69--87
\mathnet{http://mi.mathnet.ru/eng/sm2072}
\crossref{https://doi.org/10.1070/SM1986v053n01ABEH002910}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=760414}
\zmath{https://zbmath.org/?q=an:0606.30036}
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https://doi.org/10.1070/SM1986v053n01ABEH002910
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This publication is cited in the following 15 articles:
Liudmyla Kryvonos, “Polynomial Approximation of Piecewise Analytic Functions on Quasi-Smooth Arcs”, Constr Approx, 56:2 (2022), 189
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
T. A. Alexeeva, N. A. Shirokov, “Constructive description of function classes on surfaces in R3 and R4”, Probl. anal. Issues Anal., 8(26):3 (2019), 16–23
V. Andrievskii, “Application of Dzyadyk's Polynomial Kernels in the Constructive Function Theory”, Ukr Math J, 71:2 (2019), 171
Vladimir Andrievskii, “Polynomial approximation of polyharmonic functions on a complement of a John Domain”, Journal of Approximation Theory, 2014
Jafarov S.Z., “Approximation of Conjugate Functions by Trigonometric Polynomials in Weighted Orlicz Spaces”, J. Math. Inequal., 7:2 (2013), 271–281
Vladimir Andrievskii, “Approximation of Functions by Reciprocals of Polynomials on a Quasi-Smooth Arc”, SIAM J. Math. Anal, 44:4 (2012), 2329
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
Vladimir V. Andrievskii, Hans-Peter Blatt, “Polynomial Approximation of Functions on a Quasi-Smooth Arc with Hermitian Interpolation”, Constr Approx, 2009
Leonhard Frerick, Jürgen Müller, “Polynomial Approximation on Compact Sets Bounded by Dini-Smooth Arcs”, Comput. Methods Funct. Theory, 3:1 (2004), 273
V.V. Andrievskii, Handbook of Complex Analysis, 1, Geometric Function Theory, 2002, 493
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
V. V. Andrievskii, V. I. Belyi, V. V. Maimeskul, “Approximation of solutions of the equation ¯∂jf=0, j⩾1, in domain with quasiconformal boundary”, Math. USSR-Sb., 68:2 (1991), 303–323
E. B. Saff, Lecture Notes in Mathematics, 1354, Approximation and Optimization, 1988, 79
V. V. Andrievskii, “On approximation of functions by harmonic polynomials”, Math. USSR-Izv., 30:1 (1988), 1–13
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