Skip to main content
SpringerLink
Log in

Menshov representation spectra

  • Published:
Journal d’Analyse Mathématique Aims and scope

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

References

  1. F. G. Arutyunyan,Representation of measurable functions of several variables by multiple trigonometric series, Math. Sb.126; 2 (168) (1985), 267–285 (in Russian); Math. USSR Sb.54 (1986), 259–277.

    MathSciNet  Google Scholar 

  2. N. K. Bary,Trigonometricheskie ryady, Gos. Izdat. Fiz.-Mat. Lit, Moscow 1961 (in Russian);A Treatise on Trigonometric Series, Vols. I & II, Pergamon Press, New York, 1964.

    Google Scholar 

  3. V. F. Gaposhkin,The central limit theorem for some weakly dependent sequences, Theory Probab. Appl.15 (1970), 649–666.

    Article  Google Scholar 

  4. S. Kaczmarz and H. Steinhaus,Theorie der Orthogonalreihen, Warsaw, 1935.

  5. J. P. Kahane and Y. Katznelson,Sur le comportement radial des fonctions analytiques, C. R. Acad. Sci. Paris, Series I272 (1971), 718–719.

    MATH  MathSciNet  Google Scholar 

  6. B. S. Kashin,A certain complete orthonormal system, Mat. Sb.99 (1976), 356–365 (in Russian); Math. USSR-Sb.28 (1976), 315–324.

    MathSciNet  Google Scholar 

  7. N. Katz,Sommes exponentielles, Asterisque79 (1980), 1–209.

    Google Scholar 

  8. S. V. Konyagin,On the limits of indeterminacy of trigonometric series, Mat. Zametki44 (1988), 770–783 (in Russian); Math. Notes44 (1988), 910–920.

    Google Scholar 

  9. P. Koosis,Introduction to H p Spaces, Cambridge University Press, 1980.

  10. T. W. Körner,On the representation of functions by trigonometric series, Ann. Fac. Sci. Toulouse Math.6 (1996, special issue), 77–119.

    Google Scholar 

  11. G. Kozma and A. Olevskiî,Representation of non-periodic functions by trigonometric series with almost integer frequencies, C. R. Acad. Sci. Paris, Serie I329 (1999), 275–280.

    MATH  Google Scholar 

  12. G. Kozma and A. Olevskiî,An “analytic» version of Menshov's, representation theorem, C. R. Acad. Sci. Paris, Serie, I331 (2000), 219–222.

    MATH  Google Scholar 

  13. D. E. Menshov,Sur la representation des fonctions mesurables par de séries trigonometriques, Mat. Sb.9 (1941), 667–692.

    Google Scholar 

  14. D. E. Menshov,Convergence in measure of trigonometric series, Trudy Mat. Inst. Steklov32 (1950, in Russian); Amer. Math. Soc. Transl. (1)3 (1950), 197–270.

  15. A. M. Olevskiî,Modification of functions and Fourier series, Uspekhi Mat. Nauk40 (1985), 157–193 (in Russian); Russian Math Surveys40 (1985), 187–224 (English translation).

    Google Scholar 

  16. A. A. Talalyan,The representation of measurable functions by series, Uspekhi Mat. Nauk15:5 (1960), 77–41 (in Russian); Russian Math. Surveys15 (1960), 75–136.

    Google Scholar 

  17. A. A. Talalyan and R. I. Ovsepyan,The representation theorems of D. E. Men'shov and their impact on the development of the metric theory of functions, Uspekhi Mat. Nauk47:5 (287) (1992), 15–44 (in Russian); Russian Math. Surveys47 (1992), 13–47.

    MATH  MathSciNet  Google Scholar 

  18. A. Zygmund,Trigonometric Series, 2nd ed., Cambridge University Press, 1959.

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Tel Aviv University, 69979, Tel Aviv, Israel

    Gady Kozma & Alexander Olevskiî

Authors
  1. Gady Kozma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander Olevskiî
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kozma, G., Olevskiî, A. Menshov representation spectra. J. Anal. Math. 84, 361–393 (2001). https://doi.org/10.1007/BF02788115

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02788115

Keywords

Search

Navigation