Skip to main content
Log in

Certain extremal problem for nonnegative trigonometric polynomials

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature cited

  1. Ch.-J. de la Vallée Poussin, “Sur la fonction ζ(s) de Riemann et le nombre des nombre premiers inférieurs à une limite donnée,” Mem. couron. et autres Mem. publ. par Acad. Roy. Sci. Lettres et Beaus-Arts de Belgique,59, No. 1, 1–74 (1899).

    Google Scholar 

  2. E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Teubner, Leipzig, Berlin (1909).

    Google Scholar 

  3. L. Tschakaloff, “Trigonometrische Polynomme mit einer Minimumeigenschaft,” Ann. Schola Norm. Super. Pisa, Ser. 2,9, 13–26 (1940).

    Google Scholar 

  4. B. L. van der Waerden, “Uber Landau's Rewies des Primzahlsatzes,” Mathematische Zeitschrift,52, 649–653 (1949).

    Google Scholar 

  5. S. French, “Trigonometric polynomials in prime number theory,” Ill. J. Math.,10, No. 2, 240–248 (1966).

    Google Scholar 

  6. S. B. Stechkin, “On some extremal properties of positive trigonometric polynomials,” Mat. Zametki,7, No. 4, 411–422 (1970).

    Google Scholar 

  7. J. B. Rosser and L. Schoenfeld, “Approximate formulas for some functions of prime numbers,” Ill. J. Math.,6, 64–94 (1962).

    Google Scholar 

  8. S. B. Stechkin, “On the zeros of the Riemann zeta-function,” Mat. Zametki,8, No. 4, 419–429 (1970).

    Google Scholar 

  9. J. B. Rosser and L. Schoenfeld, “Sharper bounds for the Chebyshev functions θ(x) and ψ(x),” Math. Comp.,29, No. 129, 243–269 (1975).

    Google Scholar 

  10. V. P. Kondrat'ev, “On some extremal properties of positive trigonometric polynomials,” Mat. Zametki,22, No. 3, 371–374 (1977).

    Google Scholar 

  11. A. V. Reztsov, “Some extremal properties of nonnegative trigonometric polynomials,” Mat. Zametki,39, No. 2, 245–252 (1986).

    Google Scholar 

  12. N. I. Chernykh, “On Jackson's inequality in L2,” Tr. Mat. Inst. Akad. Nauk SSSR,88, 71–74 (1967).

    Google Scholar 

  13. N. I. Chernykh, “On the best approximation of periodic functions by trigonometric polynomials in L2,” Mat. Zametki,2, No. 5, 513–522 (1967).

    Google Scholar 

  14. A. G. Babenko, “On a certain extremal problem for polynomials with a fixed mean value,” in: Approximation of Functions by Polynomials and Splines [in Russian], Ural'skii Nauchnyi Tsentr Akad. Nauk SSSR, Sverdlovsk (1985), pp. 15–22.

    Google Scholar 

  15. A. G. Babenko, “On the exact constant in Jackson's inequality in L2,” Mat. Zametki,39, No. 5, 651–664 (1986).

    Google Scholar 

  16. G. Pólya and G. Szegö, Problems and Theorems in Analysis, Vol. 2, Springer-Verlag, New York (1976).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 47, No. 1, pp. 15–28, January, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arestov, V.V., Kondrat'ev, V.P. Certain extremal problem for nonnegative trigonometric polynomials. Mathematical Notes of the Academy of Sciences of the USSR 47, 10–20 (1990). https://doi.org/10.1007/BF01157278

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01157278

Keywords

Navigation