Geodesic
On the uniform polynomial approximation in complex domain summary
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part V, Tome 47 (1974), pp. 164-165 Cet article a éte moissonné depuis la source Math-Net.Ru

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The class of the so-called Faber domaines is introduced.This class contains all convex domains, all domains with the piecewise smooth boundary with the finite number of angular points and all domains with the boundary of bounded rotation. The article yields a complete description of the analytic functions $f$ in the Faber domain $G$ with $$ E_n(f;G)=O(n^{-s}),\quad s>0,\quad n\to\infty, $$ where $E_n(f;G)$ is the best polynomial approximation of degree $\leq n$. In the case of the piecewise smooth boundary with angular points this description admits a reformulation in standard metric terms. 
@article{ZNSL_1974_47_a11,
     author = {E. M. Dyn'kin},
     title = {On the uniform polynomial approximation in complex domain summary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {164--165},
     year = {1974},
     volume = {47},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1974_47_a11/}
}
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E. M. Dyn'kin. On the uniform polynomial approximation in complex domain summary. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part V, Tome 47 (1974), pp. 164-165. http://geodesic.mathdoc.fr/item/ZNSL_1974_47_a11/