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 $p$_n is not bounded, for any sequence $$w_n, decreasing to zero and not being $o(1/(ln\; p$_n+1)), the continuous function $f(t)$ with $$w_n(f) = w_n, Fourier series of which is not Poisson--Abel summable at the point, is constructed.

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Last modified: September 1, 2000