Best Polynomial Approximation in -Norm and -Growth of Entire Functions

Abstract

The classical growth has been characterized in terms of approximation errors for a continuous function on by Reddy (1970), and a compact of positive capacity by Nguyen (1982) and Winiarski (1970) with respect to the maximum norm. The aim of this paper is to give the general growth (-growth) of entire functions in by means of the best polynomial approximation in terms of -norm, with respect to the set , where is the Siciak's extremal function on an -regular nonpluripolar compact is not pluripolar.