Proof of a conjecture of Zahariuta concerning a problem of Kolmogorov on the epsilon-entropy

摘要

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