Characterization of the best uniform approximation of periodic functions by convex classes defined by strictly CVD kernels

O. Davydov, Characterization of the best uniform approximation of periodic functions by convex classes defined by strictly CVD kernels, in "Approximation Theory VIII" (C.K.Chui and L.L.Schumaker, Eds.), Vol. 1: "Approximation and Interpolation," pp. 177-184, World Scientific Publishing Co., 1995.

Abstract: We present a Chebyshev-type characterization for the best uniform approximations of periodic continuous functions by functions of the class $$ {\cal M} = \{ f(x): \enskip f(x) = \int_0^{2\pi}K(x,y) h(y)\,dy , \enskip |h(y)| \leq 1 {\rm \enskip a.\ e.} , \enskip y \in [0, 2\pi ) \} , $$ where $K(x,y)$ is a strictly cyclic variation diminishing kernel.

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