On the Growth and Approximation of Transcendental Entire Functions on Algebraic Varieties

Abstract

Let X be a complete intersection algebraic variety of codimension m > 1 in Cm+n. Inthis paper we characterized the classical growth parameters order and type for transcendental entire functions f ∈ ⊕(X), the space of holomorphic functions on the complete intersection algebraic variety X, in terms of the best polynomial approximation error in Lp-norm, 0 < p ≤ ∞, on a L − regular non-pluripolar compact subset K of Cm+n.