Kolmogorov and linear diameters of functional classes and finite dimensional sets

Galeev E. M.
Vladikavkaz Mathematical Journal 2011. Vol. 13. Issue 2.

Abstract:
In this paper we give a brief review of results concerning the Kolmogorov and linear diameters of Sobolev, Holder--Nikol'skii and Besov classes of periodic functions of one and several variables as well as of finite-dimensional sets. We present theorems for the order estimates of diameters obtained by the author, Temlyakov and others.

Keywords: approximation, classes of periodic functions of one and several variables, Kolmogorov diameters, linear diameters, imbedding of functional classes, imbedding of finite dimensional sets.

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