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 Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 1, Pages 148–164 (Mi izv2218)

The solid inverse problem of polynomial approximation of functions on a regular compactum

P. M. Tamrazov

Abstract: We solve the solid inverse problem of polynomial approximation of functions on compact of the complex plane which have a connected complement and which are regular in the sense of the solvability of the Dirichlet problem for continuous boundary values. Here the term “solid” is used to denote that the derivative and the modulus of continuity of the function are defined with regard to not only the boundary but also the interior points of the compactum.
As a very special case the results of this paper contain the solution for the solid inverse problem of polynomial approximation for arbitrary bounded continua with connected complement.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:1, 145–162

Bibliographic databases:

UDC: 517.5
MSC: 30A82

Citation: P. M. Tamrazov, “The solid inverse problem of polynomial approximation of functions on a regular compactum”, Izv. Akad. Nauk SSSR Ser. Mat., 37:1 (1973), 148–164; Math. USSR-Izv., 7:1 (1973), 145–162

Citation in format AMSBIB
\Bibitem{Tam73} \by P.~M.~Tamrazov \paper The solid inverse problem of polynomial approximation of functions on a~regular compactum \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1973 \vol 37 \issue 1 \pages 148--164 \mathnet{http://mi.mathnet.ru/izv2218} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=377068} \zmath{https://zbmath.org/?q=an:0251.30038} \transl \jour Math. USSR-Izv. \yr 1973 \vol 7 \issue 1 \pages 145--162 \crossref{https://doi.org/10.1070/IM1973v007n01ABEH001930} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. 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
2. V. V. Andrievskii, “Approximation characterization of classes of functions on continua of the complex plane”, Math. USSR-Sb., 53:1 (1986), 69–87
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