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We present a general approach to obtain direct and inverse results for approximation in Hölder norms. This approach is used to obtain a collection of new results related with estimates of the best polynomial approximation and with the approximation by linear operators of non-periodic functions in Hölder norms.
We improve the class of indices for which normality takes place in a Nikishin system and apply this in Hermite-Padé approximation of such systems of functions.
This paper is an introductory approach to several approximation problems of periodic functions in connection with Fourier series, Lipschitz functions and related topics. Traditional results in this context are presented and discussed in the first two sections. Further, we introduce certain Hölder spaces of integrable functions that become homogeneous Banach… (More)