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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2010, Number 4, Pages 7–15 (Mi vmumm794)  
Mathematics

$(C,1)$-Summation of Fourier series over rearranged Vilenkin system

I. V. Polyakov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (262 kB)
Abstract: The Cesaro means of a function $f$ with respect to the Vilenkin system in Kaczmarz rearrangement are considered. We prove that these means of a summable function converge to it almost everywhere.
Key words: Fourier series, Vilenkin system, Kaczmarz system, convergence almost everywhere, Shipp's rearrangements of Walsh system, $(C,1)$-summability.
Funding agency Grant number
Russian Foundation for Basic Research 08-01-00669
Ministry of Education and Science of the Russian Federation НШ-3252.2010.1
Received: 23.06.2008
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: I. V. Polyakov, “$(C,1)$-Summation of Fourier series over rearranged Vilenkin system”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2010, no. 4, 7–15
Citation in format AMSBIB
\Bibitem{Pol10}
\by I.~V.~Polyakov
\paper $(C,1)$-Summation of Fourier series over rearranged Vilenkin system
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2010
\issue 4
\pages 7--15
\mathnet{http://mi.mathnet.ru/vmumm794}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2759286}
\zmath{https://zbmath.org/?q=an:1304.42009}
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