# Sharp inequalities for approximations of classes of periodic convolutions by odd-dimensional subspaces of shifts

Research paper by O. L. Vinogradov

Indexed on: 07 May '09Published on: 07 May '09Published in: Mathematical Notes

#### 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.