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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 1983, Number 2, Pages 37–42
(Mi vmumm3468)
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This article is cited in 4 scientific papers (total in 4 papers)
Mathematics
Pointwise convergence of Fourier series with respect to multiplicative systems
V. I. Shcherbakov
Abstract:
We study the pointwise convergence of Fourier series with respect to multiplicative Vilenkin systems. We derive some two-sided estimates of Dirichlet kernels. We find analogies of the Dini condition for the convergence of the Fourier series at some point $x$.
In particular, we show that, whenever the condition
$$
\int_G\frac{|f(x\dotplus t)+f(x\overset{.}-t)-2f(x)|}{t}\,dt<\infty
$$
guarantees the convergence of the Fourier series $f(x)$ at $x$ the same is not true of the condition
$$
\int_G\frac{|f(x\dotplus t)-f(x)|}{t}\,dt<\infty
$$
(for unbounded systems).
Received: 27.01.1982
Citation:
V. I. Shcherbakov, “Pointwise convergence of Fourier series with respect to multiplicative systems”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1983, no. 2, 37–42
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https://www.mathnet.ru/eng/vmumm3468 https://www.mathnet.ru/eng/vmumm/y1983/i2/p37
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