2017
Том 69
№ 9

All Issues

On some extremal problems of approximation theory in the complex plane

Vakarchuk S. B.

Full text (.pdf)


Abstract

In the Hardy Banach spaces H q , Bergman Banach spaces Hq, and Banach spaces ℬ (p, q, λ), we determine the exact values of the Kolmogorov, Bernstein, Gel’fand, linear, and trigonometric n-widths of classes of functions analytic in the disk |z| < 1 and such that the averaged moduli of continuity of their r-derivatives are majorized by a certain function. For these classes, we also consider the problems of optimal recovery and coding of functions.

English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 9, pp 1371-1390.

Citation Example: Vakarchuk S. B. On some extremal problems of approximation theory in the complex plane // Ukr. Mat. Zh. - 2004. - 56, № 9. - pp. 1155-1171.

Full text