Geodesic
Sharp Inequalities for Approximations of Classes of Periodic Convolutions by Odd-Dimensional Subspaces of Shifts
Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 569-584

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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.
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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     author = {O. L. Vinogradov},
     title = {Sharp {Inequalities} for {Approximations} of {Classes} of {Periodic} {Convolutions} by {Odd-Dimensional} {Subspaces} of {Shifts}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {569--584},
     publisher = {mathdoc},
     volume = {85},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a6/}
}
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O. L. Vinogradov. Sharp Inequalities for Approximations of Classes of Periodic Convolutions by Odd-Dimensional Subspaces of Shifts. Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 569-584. http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a6/