Approximation Properties of Julia Polynomials

Let G be a finite simply connected domain in the complex plane , bounded by a rectifiable Jordan curve L, and let w = ^sub 0^ (z) be the Riemann conformal mapping of G onto D(0, r^sub 0^) := {w : |w| < r^sub 0^}, normalized by the conditions ^sub 0^ (z^sub 0^) = 0, '^sub 0^ (z^sub 0^) = 1. In this work, the rate of approximation of ^sub 0^ by the polynomials, defined with the help of the solutions of some extremal problem, in a closed domain G is studied. This rate depends on the geometric properties of the boundary L.[PUBLICATION ABSTRACT]