Proximate Growth and Best Approximation in Lp-norm of Entire Functions

Abstract

Let 0 be less than p less than infinity and Vg be the supremum of the absolute value of P in Pd, where Pd is the set of polynomials of degree less than d, and the norm of P on K is less than or equal to 1. Here, K is an L-regular compact set. The aim of this paper is to characterize the proximate growth of entire functions of several complex variables using the best polynomial approximation in the Lp-norm on an L-regular compact K.