Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Order of (C,α)-approximations on certain classes of periodic functions

  • 29 Accesses


In the spaces L and C, the orders of upper bounds for the deviations of a function and its conjugate from the Cesaro means of their Fourier series are obtained on a class of functions with a given majorant of their k-th modulus of smoothness.

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

Literature cited

  1. 1.

    N. K. Bari, Trigonometric Series [in Russian], Moscow (1961).

  2. 2.

    S. B. Stechkin, “Absolute convergence of Fourier series (second report),” Izv. Akad. Nauk SSSR, Ser. Matem.,19, No.4, 221–246 (1955).

  3. 3.

    S. B. Stechkin, “Approximation of periodic functions by Fejer sums,” Tr. Matem. In-ta Akad. Nauk SSSR,62, 48–60 (1961).

  4. 4.

    V. É. Geit, Structural and Constructive Properties of Functions and Their Conjugates [in Russian], Candidate's Dissertation, Sverdlovsk (1970).

  5. 5.

    V. É. Geit, “The accuracy of certain inequalities in the theory of approximation,” Matem. Zametki,10, No. 5, 571–582 (1971).

  6. 6.

    V. É. Geit, “Conditions for imbedding the classes H k,R ω and\(\tilde H_{k,R}^\omega\),” Matem. Zametki,13, No. 2, 169–178 (1973).

Download references

Author information

Additional information

Translated from Matematicheskie Zametki, Vol. 15, No. 1, pp. 15–20, January, 1974.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Geit, V.É. Order of (C,α)-approximations on certain classes of periodic functions. Mathematical Notes of the Academy of Sciences of the USSR 15, 9–12 (1974). https://doi.org/10.1007/BF01153537

Download citation


  • Fourier
  • Fourier Series
  • Periodic Function
  • Cesaro Means