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Optimal recovery of functions and their derivatives from Fourier coefficients prescribed with an error

G. G. Magaril-Il'yaev^a, K. Yu. Osipenko<sup>b

a</sup> Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
^b Moscow State Aviation Technological University

Abstract: The problems of the optimal recovery of functions and their derivatives from approximate values of their Fourier coefficients are considered. Explicit expressions for optimal recovery methods in classes of smooth and analytic functions defined on various compact manifolds are presented.

UDC: 517.5

MSC: Primary 41A65; Secondary 90C25, 46E20

Received: 01.11.2001

DOI: 10.4213/sm637

 English version: Sbornik: Mathematics, 2002, 193:3, 387–407

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