Uniformn-analytic polynomial approximations of functions on rectifiable contours in ℂ |
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Authors: | K Yu Fedorovskii |
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Institution: | (1) Moscow State University, USSR |
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Abstract: | We study approximations of functions byn-analytic polynomials in the uniform norm on closed rectifiable Jordan curves in the complex plane. It is shown that, in contrast
to the case of uniform approximations by complex polynomials, there are no topological criteria for the existence of such
approximations. We obtain a criterion for the existence ofn-analytic polynomial approximations in terms of analytic properties of these curves.
Translated fromMatematicheskie Zametki, Vol. 59, No. 4, pp. 603–609, April, 1996.
The author is extremely grateful to A. G. Vitushkin and P. V. Paramonov for the statement of the problem and their attention
to the work.
The work was partially supported by the Russian Foundation for Basic Research under grant No. 93-01-00225. |
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Keywords: | |
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