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

V. N. Belykh

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

Abstract: 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 $k\to\infty$.

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

UDC: 519.6+515.127

Received: 08.04.2025
Revised: 18.06.2025
Accepted: 07.07.2025

DOI: 10.25205/1560-750X-2025-28-3-5-18