FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 2, PAGES 485-500

On Poisson--Abel method of summing up Fourier series with respect to multiplicative systems

O. P. Naumov

Abstract

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The sufficient condition of Poisson--Abel summability of Fourier series with respect to multiplicative systems is obtained. If a sequence pn is not bounded, for any sequence wn, decreasing to zero and not being o(1/(ln pn+1)), the continuous function f(t) with wn(f) = wn, Fourier series of which is not Poisson--Abel summable at the point, is constructed.


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