Sur une conjecture de Zahariuta et un problème de Kolmogorov

Abstract

We prove the Zahariuta's conjecture, which itself solves a Kolmogorov's problem on the ε-entropy of classes of analytic functions. For a given holomorphically convex compact subset K in a bounded pseudoconvex domain D in C n , the Zahariuta's conjecture consists in approximating uniformly on any compact subset of D⧹ K, the relative extremal function u K, D by a sequence of pluricomplex Green functions on D with logarithmic poles in the compact set K.