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

• 成果类型: Article
• 署名作者: Nivoche, S
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0372-5
• 发表日期: 2004
• 页码: 413-450
• 关键词: extremal plurisubharmonic-functions; pluricomplex green-function; capacity; notions; sets

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.