The article is devoted to results relating to the theory of rational approximation of an analytic function. Let ƒ be an analytic function on the disk {z : |z| < ñ), ñ > 1. The rate of decrease of the best approximations ñnof a function ƒ by the rational functions of order at most n in the uniform metric on the unit disk E with the center z = 0 is investigated. The theorem connecting the rate of decrease of ñnwith the order ó > 0 of ƒ in the disk {z : |z| < ñ} is proved. The proof of this results is based on an analysis of behavior of the singular numbers of the Hankel operator constructed from the function ƒ.
Radyno, A. Y. (1998). About the rate of rational approximation of some analytic functions. Mathematical Modelling and Analysis, 3(1), 168-176. https://doi.org/10.3846/13926292.1998.9637100
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