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Best approximation and symmetric decreasing rearrangements of functions. (English. Russian original) Zbl 1155.41311
Function spaces, harmonic analysis, and differential equations. Collected papers. Dedicated to the 95th anniversary of academician S. M. Nikol’skii. Transl. from the Russian. Moscow: MAIK Nauka/Interperiodika Publishing. Proc. Steklov Inst. Math. 232, 172-186 (2001); translation from Tr. Mat. Inst. Steklova 232, 179-193 (2001).
Summary: The problem of estimating the best approximation by a subspace of classes of functions of \(n\) variables defined by restrictions imposed on the modulus of continuity is considered on the basis of the duality principle. An approach is analyzed that is connected with the representation of a function of \(n\) variables as a countable sum of simple functions and the subsequent transition to spatial symmetric decreasing rearrangements.
For the entire collection see [Zbl 0981.00017].
41A50 Best approximation, Chebyshev systems