On the zeros of polynomials of best approximation

Given a function f, uniform limit of analytic polynomials on a compact, reg ular set E subset of C-N, we relate analytic extension properties of f to t he location of the zeros ol the best polynomial approximants to f in either the uniform norm on E or in appropriate L-q norms. These results give multivariable versions of one-variable results due to Bl att-Saff, Plesniak and Wojcik. (C) 1999 Academic Press.