This article is cited in 5 papers

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.

UDC: 517.5

MSC: 30A82

Received: 23.03.1971

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

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