Skip to main content
SpringerLink
Log in

Some particular properties of general orthonormal systems

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

The present paper deals with some particular properties of special series of Fourier coefficients of the class of functions with bounded variation with respect to general orthonormal systems (ONS). The obtained results demonstrate that the properties of the general ONS and of the classical ONSs (trigonometric, Haar, Walsh system) are different in some cases.

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

Similar content being viewed by others

References

  1. L. Gogoladze, V. Tsagareishvili, Summability of general Fourier series. Publ. Math. Debr. 91(3–4), 391–402 (2017)

    Article  MathSciNet  Google Scholar 

  2. A.M. Olevskiĭ, Orthogonal series in terms of complete systems. Mat. Sb. (N.S.) 58(100), 707–748 (1962). (in Russian)

    MathSciNet  Google Scholar 

  3. S. Kaczmarz, H. Steinhaus, Theorie der Orthogonalreihen. Monografie Matematyczne 6 (Russian translation: Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1958). (Chelsea Publishing Company, New York, 1951)

  4. G. Alexits, Convergence Problems of Orthogonal Series, vol. 20, International Series of Monographs in Pure and Applied Mathematics (Pergamon Press, New York, 1961)

    MATH  Google Scholar 

  5. V. Tsagareishvili, On the Fourier coefficients of functions with respect to general orthonormal systems. Izv. Ross. Akad. Nauk Ser. Mat. 81(1), 183–202 (2017). (in Russian); translation in Izv. Math. 81(1), 179–198 (2017)

    MathSciNet  MATH  Google Scholar 

  6. V. Tsagareishvili, Absolute convergence of Fourier series of functions of the class \({\rm Lip}\,1\) and of functions of bounded variation. Izv. Ross. Akad. Nauk Ser. Mat. 76(2), 215–224 (2012). (in Russian); translation in Izv. Math. 76(2), 419–429 (2012)

    Article  MathSciNet  Google Scholar 

  7. L. Gogoladze, V. Tsagareishvili, Fourier coefficients of continuous functions. Mat. Zametki 91(5), 691–703 (2012). (in Russian); translation in Math. Notes 91(5-6), 645–656 (2012)

    Article  MathSciNet  Google Scholar 

  8. V. Tsagareishvili, G. Tutberidze, Multipliers of absolute convergence. Mat. Zametki 105(3), 433–443 (2019). (in Russian); translation in Math. Notes 105(3), 135–144 (2019)

    Article  MathSciNet  Google Scholar 

  9. Z. Ciesielski, Properties of the orthonormal Franklin system. II. Stud. Math. 27, 289–323 (1966)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Exact and Natural Sciences, I. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    V. Tsagareishvili

Authors
  1. V. Tsagareishvili
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Tsagareishvili.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tsagareishvili, V. Some particular properties of general orthonormal systems. Period Math Hung 81, 149–157 (2020). https://doi.org/10.1007/s10998-020-00323-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10998-020-00323-4

Keywords

Mathematics Subject Classification

Search

Navigation