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

Multipliers of Fourier series


New statements are proved regarding multipliers of trigonometric Fourier series in the space C of continuous periodic functions.

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

Literature cited

  1. 1.

    A. Zygmund, Trigonometric Series. Vol. I, Cambridge Univ. Press, Cambridge (1959).

  2. 2.

    R. E. Edwards, Fourier Series: A Modern Introduction, Vol. II, Holt, Rinehart and Winston, New York (1967).

  3. 3.

    R. M. Trigub, “Multipliers of Fourier series and approximation of functions by polynomials in the spaces C and L,” Dokl. Akad. Nauk SSSR, 306, No. 2, 192–296 (1989).

  4. 4.

    N. P. Korneichuk, Extremal Problems of Approximation Theory [in Russian], Nauka, Moscow (1976).

  5. 5.

    R. M. Trigub, “On the comparison principle for Fourier expansions and existence subspaces in the integral metric,” Trudy Mat. Inst. Akad. Nauk SSSR,180, 219–221 (1987).

  6. 6.

    R. M. Trigub, “Absolute convergence of Fourier integrals, summability of Fourier series and approximation by polynomials of functions on a torus,” Izv. Akad. Nauk SSSR, Ser. Mat.,44, No. 6, 1378–1409 (1980).

  7. 7.

    R. M. Trigub, “Approximation by polynomials of continuous periodic functions with bounded derivative,” in: Theory of Mapping and Approximation of Functions [in Russian], Naukova Dumka, Kiev (1989), pp. 185–195.

Download references

Author information

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 12, pp. 1686–1693, December, 1991.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Trigub, R.M. Multipliers of Fourier series. Ukr Math J 43, 1572–1578 (1991).

Download citation


  • Fourier Series
  • Periodic Function
  • Trigonometric Fourier Series
  • Continuous Periodic Function