About the rate of rational approximation of some analytic functions

    A. YA. Radyno Affiliation


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 ñn of 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 ñn with 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.

First Published Online: 14 Oct 2010

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Radyno, A. Y. (1998). About the rate of rational approximation of some analytic functions. Mathematical Modelling and Analysis, 3(1), 168-176.
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Dec 15, 1998
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