Computational Methods and Function Theory 2 (2002), No. 1, 87--112
Copyright Heldermann Verlag 2002
Optimal Recovery and Extremum Theory
Georgii G. Magaril-Il'yaev
email@example.com, Department of Higher Mathematics, Moscow State Institute of Radio Engineering, Electronics and Automation (Technology University), pr. Vernadskogo 78, 117454 Moscow, Russia.
Konstantin Yu. Osipenko
firstname.lastname@example.org, Department of Higher Mathematics, MATI --- Russian State Technological University, Orshanskaya 3, 121552 Moscow, Russia.
Vladimir M. Tikhomirov
email@example.com, Department of General Control Problems, Moscow State University, Vorob'evy Gory, 119899 Moscow, Russia.
In this paper optimal recovery problems of linear functionals on classes of smooth and analytic functions on the basis of linear information are considered from the general viewpoint of extremum theory. A general result about the connection of optimal recovery method with Lagrange multipliers of some convex extremal problem is applied to the analysis of classical recovery problems on the generalized Sobolev, Hardy, and Hardy-Sobolev classes.
Keywords: Optimal recovery, Lagrange Principle, Hardy spaces.
MSC 2000: 41A46, 30D55.
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