| Abstract: | This paper is devoted to results belonging to the theory of rational approximation of analytic functions. We study the rate of decrease of the best approximations  n of a functionf holomorphic in a disk ¦z  ¦z¦< , >1> by rational functions of order at most n in the uniform metric on the unit disk with center at z=0. We prove theorems that connect the rate of decrease of the quantities n with the order   0 and type  0 of the functionf. The proofs of these results are based on the methods of the theory of Hankel operators.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 32–39.The author is grateful to Prof. V. A. Prokhorov for posing this problem and assistance with the preparation of this article. |
