Journal d’Analyse Mathématique

, Volume 84, Issue 1, pp 361–393

Menshov representation spectra

  • Gady Kozma
  • Alexander Olevskiî


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  1. [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.MathSciNetGoogle Scholar
  2. [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. [3]
    V. F. Gaposhkin,The central limit theorem for some weakly dependent sequences, Theory Probab. Appl.15 (1970), 649–666.CrossRefGoogle Scholar
  4. [4]
    S. Kaczmarz and H. Steinhaus,Theorie der Orthogonalreihen, Warsaw, 1935.Google Scholar
  5. [5]
    J. P. Kahane and Y. Katznelson,Sur le comportement radial des fonctions analytiques, C. R. Acad. Sci. Paris, Series I272 (1971), 718–719.MATHMathSciNetGoogle Scholar
  6. [6]
    B. S. Kashin,A certain complete orthonormal system, Mat. Sb.99 (1976), 356–365 (in Russian); Math. USSR-Sb.28 (1976), 315–324.MathSciNetGoogle Scholar
  7. [7]
    N. Katz,Sommes exponentielles, Asterisque79 (1980), 1–209.Google Scholar
  8. [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. [9]
    P. Koosis,Introduction to H p Spaces, Cambridge University Press, 1980.Google Scholar
  10. [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. [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.MATHGoogle Scholar
  12. [12]
    G. Kozma and A. Olevskiî,An “analytic» version of Menshov's, representation theorem, C. R. Acad. Sci. Paris, Serie, I331 (2000), 219–222.MATHGoogle Scholar
  13. [13]
    D. E. Menshov,Sur la representation des fonctions mesurables par de séries trigonometriques, Mat. Sb.9 (1941), 667–692.Google Scholar
  14. [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.Google Scholar
  15. [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. [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. [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.MATHMathSciNetGoogle Scholar
  18. [18]
    A. Zygmund,Trigonometric Series, 2nd ed., Cambridge University Press, 1959.Google Scholar

Copyright information

© The Hebrew University Magnes Press 2001

Authors and Affiliations

  • Gady Kozma
    • 1
  • Alexander Olevskiî
    • 1
  1. 1.School of MathematicsTel Aviv UniversityTel AvivIsrael

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