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 $\text{C}{}^{\mathrm{n}}$, 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.