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