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  • Author or Editor: A. A. Dovgoshei x
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Abstract  

For compact setsK
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$K \subseteq C$$ \end{document}
C of zero logarithmic capacity we obtain the analogue of the well-known Bernstein-Walsh theorem that describes the relation between the decreasing rate of the best uniform polynomial approximation to a functionf onK and the possibility of its analytic extension into the “canonical” domain bounded by the level line of the Green functiongK.
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