Abstract
Sharp Akhiezer-Krein-Favard-type inequalities for classes of periodic convolutions with kernels that do not increase oscillation are obtained. A large class of approximating odd-dimensional subspaces constructed from uniform shifts of one function with extremal widths is specified. As a corollary, sharp Jackson-type inequalities for the second-ordermodulus of continuity are derived.
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Original Russian Text © O. L. Vinogradov, 2009, published in Matematicheskie Zametki, 2009, Vol. 85, No. 4, pp. 569–584.
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Vinogradov, O.L. Sharp inequalities for approximations of classes of periodic convolutions by odd-dimensional subspaces of shifts. Math Notes 85, 544–557 (2009). https://doi.org/10.1134/S0001434609030250
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DOI: https://doi.org/10.1134/S0001434609030250