Mathematical Notes

, Volume 100, Issue 3–4, pp 472–476 | Cite as

On the rate of convergence in L of Fourier sine series with monotone coefficients

Article
  • 22 Downloads

Abstract

It is shown that the exact order of decrease of the norm in L of the remainder of a Fourier sine series with monotone coefficients can be expressed in terms of the coefficients of the series just as for a series with convex coefficients. But the numerical multipliers in the estimates are different.

Keywords

convergence in L sine series with monotone coefficients 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Zygmund, Trigonometric Series (Cambridge Univ. Press, Cambridge, 1959; Mir, Moscow, 1965), Vol. 1.MATHGoogle Scholar
  2. 2.
    R. E. Edwards, Fourier Series: A Modern Introduction (Springer-Verlag, Heidelberg, 1982; Mir, Moscow, 1985), Vol. 1.CrossRefMATHGoogle Scholar
  3. 3.
    S. A. Telyakovskii and G. A. Fomin, “On the convergence in the L-metric of Fourier series with quasi-monotone coefficients,” in Trudy Mat. Inst. Steklov, Vol. 134: Theory of Functions and Its Applications [MIAN, Moscow, 1975], pp. 310–313 [Proc. Steklov Inst. Math. 134, 351–355 (1977)].Google Scholar
  4. 4.
    S. A. Telyakovskii, “An estimate of the norm of a function by its Fourier coefficients that is suitable in problems of approximation theory,” in Trudy Mat. Inst. Steklov, Vol. 109: Approximation of Periodic Functions [MIAN, Moscow, 1971], pp. 65–97.Google Scholar
  5. 5.
    S. A. Telyakovskii, “Approximation of differentiable functions by partial sums of their Fourier series,” Mat. Zametki 4 (3), 291–300 (1968).MathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

Personalised recommendations