Sharp Inequalities for Approximations of Classes of Periodic Convolutions by Odd-Dimensional Subspaces of Shifts

O. L. Vinogradov

Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 569-584.

Résumé

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-order modulus of continuity are derived.

Détail

Keywords: Akhiezer–Krein–Favard inequality, periodic convolution, Jackson inequality, second-order modulus of continuity, the space $L_p$, Sobolev class, spline.

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