Abstract :
LetE⊂Cnbe compact, regular, and polynomially convex with pluricomplex Green functionVE. Given a sequence of polynomials {pj}j=1, 2, …, the first result is a condition for (limj→∞(log |pj(z)|/deg(pj)))* to equalVEon Cn−E. The condition involves the Robin function ofEand the highest order homogeneous terms of thepjand generalizes one-variable results of Blatt–Saff. A second result gives a necessary and sufficient condition forf, the uniform limit of polynomials onE, to extend holomorphically toER={z | VE(z)1. The condition involves highest order homogeneous terms of best approximating polynomials tofand the Robin function ofEand extends results of Szczepański.
