On estimating the value of the Alexandrov`s width of a compact from below infinitely smooth aperiodic functions of the Gevrey's class

Belykh Vladimir Nikitych

0000 0002 4428 3087

Scopus Author ID: 700 404 6309

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

belykh@math.nsc.ru

A bottom-down estimate of decreasing to zero at $n\to\infty$ of the Alexandrov's $n$-width of a compact aperiodic $C^\infty$-smooth Gevrey's functions of class $\alpha\ge 1$ is calculated, determined by the growth pattern of the majorant of the $k$-th derivatives of its elements at $k\to\infty$.

УДК 519.6+515.127

Keywords: compact set, Gevrey's class, topological dimension, Alexandrov's width, amount of smoothness, unsaturation.