Approximation of Periodic Functions by the Euler and Borel Means of Fourier Series

Abstract

Dedicated to the memory of Professor Roman Sikorskt1. Preliminaries Let L and C be the spaoes composed of all 2jr-periodic complex-valued functions Lebesgue-integrable on the interval ^0,2jt> and all 2jr-periodic complex-valued functions continuous in<0,2jn>, respectively.Introduce in these spaoes the usual normsDenote by M the set of all bounded functions belonging to L. Suppose that $ is a continuous, convex and strictly increasing function in the interval <0, 00 ), such that$(0) = 0. Given any function fe M, let us denote by V^(fja,b) the total ^-variation of f on the interval <a,b>, defined as the upper bound of the set of non-negative numbers

Locations

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