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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 2, Pages 243–261 (Mi izv1659)  

This article is cited in 6 scientific papers (total in 6 papers)

Direct theorems of approximation theory on quasiconformal arcs

V. V. Andrievskii


Abstract: This paper studies the polynomial approximation of functions that are continuous on an arbitrary finite quasiconformal arc.
Bounds are obtained for the degree of approximation, including bounds depending on the position of the point at which the deviation of the approximating polynomial from the given function is studied, and also uniform bounds (independent of the point).
The bounds of the first kind extend results of Dzyadyk, Lebedev and Shirokov, and Kolesnik to arbitrary quasiconformal arcs, which may, in particular, have no rectifiable subarcs. The bounds of the second kind are analogs of the results that Dzjadyk and Alibekov established for piecewise smooth arcs without cusps.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 16:2, 221–238

Bibliographic databases:

UDC: 517.53
MSC: Primary 30E10; Secondary 30C60
Received: 07.12.1978

Citation: V. V. Andrievskii, “Direct theorems of approximation theory on quasiconformal arcs”, Izv. Akad. Nauk SSSR Ser. Mat., 44:2 (1980), 243–261; Math. USSR-Izv., 16:2 (1981), 221–238

Citation in format AMSBIB
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\by V.~V.~Andrievskii
\paper Direct theorems of approximation theory on quasiconformal arcs
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 2
\pages 243--261
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=571097}
\zmath{https://zbmath.org/?q=an:0459.30031|0432.30030}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 16
\issue 2
\pages 221--238
\crossref{https://doi.org/10.1070/IM1981v016n02ABEH001299}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MK40900001}


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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, “Approximation characterization of classes of functions on continua of the complex plane”, Math. USSR-Sb., 53:1 (1986), 69–87  mathnet  crossref  mathscinet  zmath
    2. 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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Vladimir Andrievskii, Hans-Peter Blatt, “Erdős–Turán Type Theorems on Quasiconformal Curves and Arcs”, Journal of Approximation Theory, 97:2 (1999), 334  crossref
    4. Vladimir Andrievskii, “On the Approximation of a Continuum by Lemniscates”, Journal of Approximation Theory, 105:2 (2000), 292  crossref
    5. Vladimir Andrievskii, “Polynomial approximation of piecewise analytic functions on a compact subset of the real line”, Journal of Approximation Theory, 161:2 (2009), 634  crossref
    6. Vladimir Andrievskii, “Approximation of Functions by Reciprocals of Polynomials on a Quasi-Smooth Arc”, SIAM J. Math. Anal, 44:4 (2012), 2329  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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