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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2009, Volume 9, Issue 3, Pages 7–14
DOI: https://doi.org/10.18500/1816-9791-2009-9-3-7-14 (Mi isu53) 		 
Mathematics

Absolute convergence of single and double Fourier series on multiplicative systems

S. S. Volosivets

Saratov State University, Chair of Theory of Functions and Approximations
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DOI: https://doi.org/10.18500/1816-9791-2009-9-3-7-14
Abstract: Two-dimensional analogs of famous Zygmund and Szasz tests for absolute convergence of Fourier–Vilenkin series are established. Also it is proved that two-dimensional Szasz test is the best possible in the certain sense.
Key words: absolute convergence, Fourier–Vilenkin series, modulus of continuity, functions of bounded $p$-fluctuation.
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: S. S. Volosivets, “Absolute convergence of single and double Fourier series on multiplicative systems”, Izv. Saratov Univ. Math. Mech. Inform., 9:3 (2009), 7–14
Citation in format AMSBIB
\Bibitem{Vol09}
\by S.~S.~Volosivets
\paper Absolute convergence of single and double Fourier series on multiplicative systems
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2009
\vol 9
\issue 3
\pages 7--14
\mathnet{http://mi.mathnet.ru/isu53}
\crossref{https://doi.org/10.18500/1816-9791-2009-9-3-7-14}
\elib{https://elibrary.ru/item.asp?id=12876539}
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    		Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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