An estimate for the Siciak extremal function - Subanalytic geometry approach

摘要

We study the Lojasiewicz-Siciak inequality in C-N. This concerns the estimating from below the Siciak extremal function which is very much related to the Green function in C. As an application we present some results describing how fast holomorphic functions defined in a neighbourhood of a compact holomorphic polyhedron can be approximated uniformly on this polyhedron by complex polynomials. (C) 2015 Elsevier Inc. All rights reserved.