Moscow University Mathematics Bulletin

, Volume 74, Issue 5, pp 195–197 | Cite as

Some Convergence Tests for Fourier Series with Respect to Vilenkin System in the Case of Unbounded pk

  • S. M. VoronovEmail author
Brief Communications


Series with respect to a system of characters of a zero-dimensional compact Abelian group are considered. A generalization of an analogue of Dini test and its corollary obtained earlier for systems determined by bounded sequences {pk} are proved.


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    G. N. Agaev, N. Ya. Vilenkin, G. M. Dzhafarli, and A. I. Rubinshtein, Multiplicative Systems of Functions and Harmonic Analysis on Zero-Dimensional Groups (Elm, Baku, 1981) [in Russian].zbMATHGoogle Scholar
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    G. M. Dzhafarli. “The Convergence of Fourier Series with Respect to a Class of Orthonormal Multiplicative Systems,” Izv. Akad. Nauk AzSSR. Ser. Fiz.-Mat. Tekh. Nauk. 4, 17 (1962).MathSciNetGoogle Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Dmitry Mendeleev University of Chemical Technology of RussiaMoscowRussia

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