Interpolation characteristics of maximal polynomial approximants to rational functions

Kurzfassung/Abstract

Let E be a compact set in C with connected regular complement and let
pn, n 2 N, be a sequence of polynomials which converge maximally to a fixed rational function f on E. Then pn has n+o(n) interpolation points to f in C and the normalized counting measure n of these interpolation points (resp. its balayage measure bn onto the boundary of E) converges to the equilibrium measure of E as n ! 1. Furthermore, we prove a complete characterization of maximal convergence by interpolation.