Skip to main content
SpringerLink
Log in

Completeness of the trigonometric system for the classes ϕ(L)

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We obtain a necessary and sufficient condition for the completeness of the trigonometric system with gaps for the classes ϕ(L).

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

Similar content being viewed by others

References

  1. P. L. Ul’anov, “The representation of functions by series and the classes ϕ(L),” Uspekhi Mat. Nauk 27(2), 3–52 (1972) [Russian Math. Surveys 27 (2), 1–54 (1972)].

    Google Scholar 

  2. V. I. Ivanov, “Representation of functions by series in metric symmetric spaces without linear functionals,” in Proc. Steklov Inst. Math. (Nauka, Moscow, 1989), Vol. 189, pp. 34–77 [in Russian].

    Google Scholar 

  3. V. I. Filippov, “Linear continuous functionals and representation of functions by series in the spaces E ϕ,” Anal. Math. 27(4), 239–260 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. A. Talalyan, “Representation of functions of classes L p[0, 1], 0 < p < 1, by orthogonal series,” Acta Math. Academ. Sci. Hungar. 21(1–2), 1–9 (1970).

    MATH  Google Scholar 

  5. K. de Leeuw, “The failure of spectral analysis in L p for 0 < p < 1,” Bull. Amer. Math. Soc. 82(1), 111–114 (1976).

    Article  MATH  MathSciNet  Google Scholar 

  6. J. H. Shapiro, “Subspaces of L p(G) spanned by characters: 0 < p < 1,” Israel J. Math. 29(2–3), 248–264 (1978).

    MATH  MathSciNet  Google Scholar 

  7. A. B. Aleksandrov, “Essays on nonlocally convex Hardy classes,” in Complex Analysis and Spectral Theory, in Lecture Notes in Math. (Springer-Verlag, Berlin, 1981), Vol. 864, pp. 1–89.

    Chapter  Google Scholar 

  8. V. I. Ivanov and V. A. Yudin, “On the trigonometric system in L p, 0 < p < 1,” Mat. Zametki 28(6), 859–868 (1980).

    MATH  MathSciNet  Google Scholar 

  9. V. I. Ivanov, “Representation of measurable functions by multiple trigonometric series,” in Proc. Steklov Inst. Math. (Nauka, Moscow, 1983), Vol. 164, pp. 100–123 [in Russian].

    Google Scholar 

  10. D. Ya. Spivakovskaya, “On the trigonometric system in the metric spaces L Ψ,” Vestnik Dnepropetrovsk. Nats. Univ., No. 6, 101–115 (2001).

  11. A. Zygmund, Trigonometric Series (Cambridge Univ. Press, Cambridge, 1959, 1960; Mir, Moscow, 1965), Vols. 1, 2.

    MATH  Google Scholar 

  12. M. A. Krasnosel’skii and Ya. B. Rutitskii, Convex Functions and Orlicz Spaces (Fizmatgiz, Moscow, 1958) [in Russian].

    Google Scholar 

  13. R. M. Trigub and E. S. Belinsky, Fourier Analysis and Approximation of Functions (Kluwer Acad. Publ., Dordrecht, 2004).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Donetsk National University, Ukraine

    Yu. S. Kolomoitsev

Authors
  1. Yu. S. Kolomoitsev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © Yu. S. Kolomoitsev, 2007, published in Matematicheskie Zametki, 2007, Vol. 81, No. 5, pp. 707–712.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kolomoitsev, Y.S. Completeness of the trigonometric system for the classes ϕ(L). Math Notes 81, 632–637 (2007). https://doi.org/10.1134/S0001434607050082

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434607050082

Key words

Search

Navigation