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Exact Jackson-Stechkin inequalities and diameters of classes of functions from \(L_{2} (\mathbb R^{2} ,e^{-x^2 -y^2})\). (English. Russian original) Zbl 1145.41003
Russ. Math. 51, No. 2, 1-7 (2007); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2007, No. 2, 3-9 (2007).
In [V. A. Abilov and M. V. Abilov, Math. Notes, 57, No. 1, 3–14 (1995; Zbl 0836.41006)] the order of the width of the class \(W^{\alpha}_2H_r^{\omega}\) for the case \(r=1,\omega(\frac{1}{n})=n^{-1/2},\) was found. Here the author calculated the exact value of the width for an arbitrary nonnegative function \(\omega(\delta)\) with any \(r,\alpha\geq 0.\) Moreover, a related exact Jackson-Stechkin inequality is proved.

41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiń≠-type inequalities)
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
Full Text: DOI
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