About the rate of rational approximation of some analytic functions

Abstract

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 ñ_n 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 ñ_n 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