Skip to main content
SpringerLink
Log in

Determining the Jump of a Function of m-Harmonic Bounded Variation by Its Fourier Series

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract—

In this article, the well-known formula for determining the jump of a periodic function using the derivative of the partial sums of its Fourier series is extended to a new class of functions.

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. A. A. Kel’zon, “On functions of (m, Φ)-bounded variation,” Sov. Math., Dokl. 44 (3), 768–770 (1992).

    MathSciNet  Google Scholar 

  2. A. A. Kel’zon, “Functions of (m, Φ)-bounded variation and the convergence of Fourier series,” Russ. Math. 38 (8), 28–37 (1994).

    MathSciNet  Google Scholar 

  3. D. Waterman, “On convergence of Fourier series of functions of generalized bounded variation,” Stud. Math. 44, 107–117 (1972). https://doi.org/10.4064/sm-44-2-107-117

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Avdispahić, “On the determination of the jump of a function by its Fourier series,” Acta Math. Hung. 48 (3‒4), 267–271 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  5. G. Kvernadze, “Determination of the jumps of a bounded function by its Fourier series,” J. Approx. Theory 92, 167–190 (1998). https://doi.org/10.1006/jath.1997.3125

    Article  MathSciNet  MATH  Google Scholar 

  6. L. Fejér, “Über die Bestimmung des Sprunges der Funktion aus Fourier-Reihe,” J. Reine Angew. Math. 142 (1), 165–188 (1912).

    MATH  Google Scholar 

  7. P. Czillag, “Über die Fourierkonstanten einer Funktion von Beschränkter Schwankung,” Mat. Phys. Lapok 27, 301–308 (1918).

    Google Scholar 

  8. B. I. Golubov, “Determination of the jump of a function of bounded p-variation by its Fourier series,” Math. Notes Acad. Sci. USSR 12, 444–449 (1972). https://doi.org/10.1007/BF01094388

    Article  MathSciNet  MATH  Google Scholar 

  9. A. A. Kel’zon, “Determination of the jump of a function of generalized bounded variation from the derivatives of the partial sums of its Fourier series,” Math. Notes 99, 46–51 (2016). https://doi.org/10.1134/S0001434616010053

    Article  MathSciNet  MATH  Google Scholar 

  10. G. M. Fikhtengol’ts, Course of Differential and Integral Calculus (St. Petersburg, Lan’, 1997).

  11. N. K. Bari, Trigonometric Series (Fizmatgiz, Moscow, 1961).

    Google Scholar 

  12. I. P. Natanson, Constructive Theory of Functions (GITTL, Moscow, 1949).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Admiral Makarov State University of Maritime and Inland Shipping, 198035, St. Petersburg, Russia

    A. A. Kelzon

Authors
  1. A. A. Kelzon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Kelzon.

Ethics declarations

The author declares that he has no conflicts of interest.

Additional information

Translated by O. Pismenov

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kelzon, A.A. Determining the Jump of a Function of m-Harmonic Bounded Variation by Its Fourier Series. Russ Math. 67, 35–40 (2023). https://doi.org/10.3103/S1066369X23050043

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X23050043

Keywords:

Search

Navigation