On the Zeros of Polynomials of Best Approximation

Given a function f, uniform limit of analytic polynomials on a compact, regular set E^N, we relate analytic extension properties of f to the location of the zeros of 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 Blatt–Saff, Pleniak and Wójcik.