About the rate of rational approximation of some analytic functions

摘要

The article is devoted to results relating to the theory of rational approximation of an analytic function. Let #x192; be an analytic function on the disk {z : z #xF1;),#xF1; 1. The rate of decrease of the best approximations#xF1;nof a function #x192; by the rational functions of order at mostnin the uniform metric on the unit diskEwith the centerz= 0 is investigated. The theorem connecting the rate of decrease of#xF1;nwith the order#xF3; 0 of #x192; in the disk {z : z #xF1;} 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 #x192;.