Skip to main content
SpringerLink
Log in

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

  • Brief Communications
  • Published:
Moscow University Mathematics Bulletin Aims and scope

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

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

    Google Scholar 

  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].

    MATH  Google Scholar 

  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).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dmitry Mendeleev University of Chemical Technology of Russia, Miusskaya sq., 9, Moscow, 125047, Russia

    S. M. Voronov

Authors
  1. S. M. Voronov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. M. Voronov.

Additional information

Russian Text © The Author(s), 2019, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika. 2019, Vol. 74, No. 5, pp. 42–44.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Voronov, S.M. Some Convergence Tests for Fourier Series with Respect to Vilenkin System in the Case of Unbounded pk. Moscow Univ. Math. Bull. 74, 195–197 (2019). https://doi.org/10.3103/S0027132219050048

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027132219050048

Search

Navigation