On Kolmogorov’s ε-Entropy for a Compact Set of Infinitely Differentiable Aperiodic Functions (Babenko’s Problem)

V. N. Belykh
Translated by I. Ruzanova

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia

Correspondence to: e-mail: belykh@math.nsc.ru

Received 11 April, 2018

Abstract—The asymptotics of Kolmogorov’s $\varepsilon $-entropy for a compact set of infinitely differentiable aperiodic functions that are boundedly embedded in the space of continuous functions on a finite interval is calculated.

DOI: 10.1134/S1064562418060066