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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
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Abstract

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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References

  1. 1.
    N. Va. Yilenkin. “On a Class of Complete Orthogonal Systems,” Izvestiya Akad. Nauk SSSR., Ser. Matem. 11 (4), 363 (1947).Google Scholar
  2. 2.
    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
  3. 3.
    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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