Geodesic
Approximation characterization of classes of functions on continua of the complex plane
Sbornik. Mathematics, Tome 53 (1986) no. 1, pp. 69-87

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One possible method is suggested for the constructive description of function classes defined on continua of the complex plane for which the traditional (in this subject area) description in terms of distances from boundary points to corresponding level curves of the outer Riemann function generally does not exist. The main idea of the constructions and results presented consists in taking account of the growth of derivatives of polynomials approximating the function. Bibliography: 28 titles. 
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V. V. Andrievskii. Approximation characterization of classes of functions on continua of the complex plane. Sbornik. Mathematics, Tome 53 (1986) no. 1, pp. 69-87. http://geodesic.mathdoc.fr/item/SM_1986_53_1_a3/