Geodesic
The Gonchar-Stahl $\rho^2$-theorem and associated directions in the theory of rational approximations of analytic functions
Sbornik. Mathematics, Tome 207 (2016) no. 9, pp. 1236-1266

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The Gonchar-Stahl $\rho^2$-theorem characterizes the rate of convergence of best uniform (Chebyshev) rational approximations (with free poles) for one basic class of analytic functions. The theorem itself, modifications and generalizations of it, methods involved in its proof and other related details constitute an important subfield in the theory of rational approximations of analytic functions and complex analysis. This paper briefly outlines the essentials of the subfield. The fundamental contributions of A. A. Gonchar and H. Stahl are at the heart of the exposition. Bibliography: 70 titles.
Keywords: rational approximations, equilibrium distributions, stationary compact set, $S$-property.
Mots-clés : Padé approximants, orthogonal polynomials 
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E. A. Rakhmanov. The Gonchar-Stahl $\rho^2$-theorem and associated directions in the theory of rational approximations of analytic functions. Sbornik. Mathematics, Tome 207 (2016) no. 9, pp. 1236-1266. http://geodesic.mathdoc.fr/item/SM_2016_207_9_a2/