Advertisement

Periodica Mathematica Hungarica

, Volume 59, Issue 2, pp 203–212 | Cite as

On the convergence and Cesàro summability of trigonometric Fourier series of monotone type functions

  • David TsirekidzeEmail author
Article
  • 61 Downloads

Abstract

The behaviour of the Cesàro means of trigonometric Fourier series of monotone type functions in the space of continuous functions is studied.

Key words and phrases

trigonometric system Cesàro means summability 

Mathematics subject classification numbers

42A20 42A24 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    T. Akhobadze, On the convergence of generalized Cesàro means of trigonometric series. I, Acta Math. Hungar., 115 (2007), 59–78.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    T. Akhobadze, On the convergence of generalized Cesàro means of trigonometric series. II, Acta Math. Hungar., 115 (2007), 79–100.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    N. Bari and S. Stechkin, The best approximations and differential properties of two conjugate functions, Moskow Math. Society, 5 (1956), 483–522 (in Russian).zbMATHGoogle Scholar
  4. [4]
    L. Fejér, Untersuchungen über Fouriersche Reihen, Math. Ann., 58 (1904), 51–69.zbMATHCrossRefGoogle Scholar
  5. [5]
    L. Leindler, On the degree of approximation of continuous functions, Acta Math. Hungar., 104 (2004), 105–113.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    L. Leindler, Necessary and sufficient conditions for uniform convergence and boundedness of general class of sine series, Aust. J. Math. Anal. Appl., 4 (2007), no. 1, Art. 10, 4 pp. (electronic).Google Scholar
  7. [7]
    F. Móricz, Approximation by the partial sums of Fourier series on the one- and two-dimensional torus, Functions, series, operators (Budapest, 1999), János Bolyai Math. Soc., Budapest, 2002, 297–319.Google Scholar
  8. [8]
    M. Riesz, Sur la sommation des séries de Fourier, Acta Sci. Math. (Szeged), 1 (1923), 104–113.Google Scholar
  9. [9]
    V. Totik, On the strong approximation by (C, α)-means of Fourier series. I., Anal. Math., 6 (1980), 57–85.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    V. Totik, On the strong approximation by (C,α)-means of Fourier series. II., Anal. Math., 6 (1980), 165–184.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    L. Zhizhiashvili, On trigonometric Fourier series, Mat. Sbornik, 100 (1976), 580–609 (in Russian).Google Scholar
  12. [12]
    L. Zhizhiashvili, Some problems about trigonometric series and its conjugates, Tbilisi University Press, 1993 (in Russian).Google Scholar
  13. [13]
    A. Zygmund, Sur la sommabilité des séries de Fourier des fonctions vérifiant la condition de Lipshitz, Bull. de L’Acad. Polonaise (1925), 1–9.Google Scholar
  14. [14]
    A. Zygmund, Trigonometric series, Vol. 1, Cambridge University Press, Cambridge, 1959.zbMATHGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2009

Authors and Affiliations

  1. 1.Faculty of Exact and Natural SciencesI. Javakhishvili Tbilisi State UniversityTbilisiGeorgia

Personalised recommendations