On best rational approximation of analytic functions

Abstract

This paper contains some theorems related to the best approximation ρ n ( f ; E ) to a function f in the uniform metric on a compact set E ⊂ C ¯ by rational functions of degree at most n. We obtain results characterizing the relationship between ρ n ( f ; K ) and ρ n ( f ; E ) in the case when complements of compact sets K and E are connected, K is a subset of the interior Ω of E, and f is analytic in Ω and continuous on E.