An estimate for the Siciak extremal function – Subanalytic geometry approach

We study the Łojasiewicz–Siciak inequality in CNCN. This concerns the estimating from below the Siciak extremal function which is very much related to the Green function in CC. 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.