Skip to main content
SpringerLink
Log in

Growth of degrees of polynomial bases

  • 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

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Literature cited

  1. G. Faber, “Über die interpolatorische Darstellung stetiger Funktionen,” Jber. Deutsch. Math.-Verein.,23, 192–210 (1914).

    Google Scholar 

  2. P. L. Ul'yanov, “On some solved and unsolved problems in the theory of orthogonal series,” in: Proc. IVth All-Union Mathematical Congress [in Russian], Vol. 2, Izd. Akad. Nauk SSSR, Leningrad (1964), pp. 694–704.

    Google Scholar 

  3. R. E. Edwards, Fourier Series. A Modern Introduction [Russian translation], Mir, Moscow (1985).

    Google Scholar 

  4. P. L. Ul'yanov, “Metric theory of functions,” Tr. Mat. Inst. Akad. Nauk SSSR,182, 180–244 (1988).

    Google Scholar 

  5. G. Foias and I. Singer, “Some remarks on strongly linearly independent sequences and bases in Banach spaces,” Rev. Roumaine Math. Pures Appl.,6, No. 3, 589–594 (1961).

    Google Scholar 

  6. K. M. Shaidukov, “On the order of growth of degrees of a polynomial basis,” Funkts. Anal. Teor. Funkts. (Kazan'), No. 1, 134–138 (1963).

    Google Scholar 

  7. P. L. Ul'yanov, “Solved and unsolved problems in the theory of trigonometric and orthogonal series,” Usp. Mat. Nauk,19, No. 1, 3–69 (1964).

    Google Scholar 

  8. Z. A. Chanturiya, “On bases of the space of continuous functions,” Mat. Sb.,88, No. 4, 589–608 (1972).

    Google Scholar 

  9. Z. A. Chanturiya, “On a generalization of G. Faber's theorem about polynomial bases,” Mat. Zametki,2, No. 2, 187–190 (1967).

    Google Scholar 

  10. M. I. Kadets, “On relative projection constants and a theorem of Z. A. Chanturiya,” Soobshch. Akad. Nauk GruzSSR, No. 3, 541–543 (1974).

    Google Scholar 

  11. V. N. Temlyakov, “On the order of growth of degrees of a polynomial basis of the space of continuous functions,” Mat. Zametki,22, No. 2, 711–721 (1977).

    Google Scholar 

  12. S. V. Bochkarev, “Construction of an interpolation dyadic basis in the space of continuous functions based on the Fejer kernel,” Tr. Mat. Inst. Akad. Nauk SSSR,172, 29–59 (1985).

    Google Scholar 

  13. P. K. Suetin, Classical Orthogonal Polynomials [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  14. S. N. Bernshtein, “On the absolute maximum of a trigonometric sum,” in: Collected Works [in Russian], Izd. Akad. Nauk SSSR, Moscow (1954), pp. 127–129.

    Google Scholar 

  15. A. Zygmund, Trigonometric Series [Russian translation], Vol. II, Mir, Moscow (1965).

    Google Scholar 

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

    Google Scholar 

  17. Al. A. Privalov, “On the growth of degrees of polynomial bases and approximation of trigonometric projectors,” Mat. Zametki,42, No. 2, 207–214 (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Technological Institute of Light Industry, USSR

    Al. A. Privalov

Authors
  1. Al. A. Privalov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 48, No. 4, pp. 69–78, October, 1990.

The author is indebted to S. B. Stechkin for his attention to this paper.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Privalov, A.A. Growth of degrees of polynomial bases. Mathematical Notes of the Academy of Sciences of the USSR 48, 1017–1024 (1990). https://doi.org/10.1007/BF01139602

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01139602

Keywords

Search

Navigation