Mathematics

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

I. V. Polyakov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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.

UDC: 517.5

Received: 23.06.2008

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