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Duality of extremal problems in function spaces and approximation of functions. (English. Russian original) Zbl 0645.42003
Russ. Math. Surv. 40, No. 4, 175-176 (1985); translation from Usp. Mat. Nauk 40, No. 4(244), 195-196 (1985).
Let \(R_ n\) be an N-dimensional subspace of \(L_ p[0,2\pi]\), \(1\leq p\leq \infty\). The author considers in this brief communication ideas and methods based on duality of entremal problems in a normed linear space; and points out that such methods have made it possible to obtain the majority of precise results connected with the determination of an upper bound of best approximations on classes of functions.
Reviewer: S.M.Shah
MSC:
42A10 Trigonometric approximation
41A15 Spline approximation
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