Generalized Order and Best Approximation of Entire Function in Lp-Norm

Abstract EN

The aim of this paper is the characterization of the generalized growth of entire functions of several complex variables by means of the best polynomial approximation and interpolation on a compact K with respect to the set Ωr={z∈Cn; expVK(z)≤r}, where VK=sup{(1/d)ln|Pd|,Pd polynomial of degree≤d, ‖Pd‖K≤1} is the Siciak extremal function of a L-regular compact K.