Abstract
In the Hardy Banach spaces H q , Bergman Banach spaces H′q, 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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 9, pp. 1155–1171, September, 2004.
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Vakarchuk, S.B. On some extremal problems of approximation theory in the complex plane. Ukr Math J 56, 1371–1390 (2004). https://doi.org/10.1007/s11253-005-0122-x
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DOI: https://doi.org/10.1007/s11253-005-0122-x