We construct the best linear methods of approximation for functions of the Hardy space H p on compact subsets of the unit disk. It is shown that the Takenaka-Malmquist systems are optimal systems of functions orthonormal on the unit circle for the construction of the best linear methods of approximation.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 636–646, May, 2008.
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Savchuk, V.V. Best linear methods of approximation and optimal orthonormal systems of the Hardy space. Ukr Math J 60, 730–743 (2008). https://doi.org/10.1007/s11253-008-0091-y
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DOI: https://doi.org/10.1007/s11253-008-0091-y