Abstract:
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 $\omega_n$, decreasing to zero and not being $o(\frac{1}{\ln p_{n+1}})$, the continuous function $f(t)$ with $\omega_n(f)=\omega_n$, Fourier series of which is not Poisson–Abel summable at the point, is constructed.
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