Extendible bases and Kolmogorov problem on asymptotics of entropy and widths of some class of analytic functions

Abstract

Let K be a compact set in an open set D on a Stein manifold Ω of dimension n. We denote by H ∞ D the Banach space of all bounded and analytic in D functions endowed with the uniform norm and by A K D a compact subset of the space CK consisted of all restrictions of functions from the unit ball 𝔹 H ∞ D . In 1950ies Kolmogorov posed a problem: does