Limits of indeterminacy of trigonometric series

  • S. V. Konyagin
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Literature cited

  1. 1.
    D. E. Menchoff, “Sur la représentation des fonctions measurables par des series trigonométriques,” Mat. Sb.,9, No. 3, 667–692 (1941).Google Scholar
  2. 2.
    D. E. Men'shov, “On limits of indeterminacy of Fourier series,” Mat. Sb.,30, No. 3, 601–650 (1952).Google Scholar
  3. 3.
    N. K. Bari, Trigonometric Series [in Russian], Fizmatgiz, Moscow (1961).Google Scholar
  4. 4.
    N. N. Luzin, Integral and Trigonometric Series [in Russian], GITTL, Moscow-Leningrad (1951).Google Scholar
  5. 5.
    J. Marcinkiewicz and A. Zygmund, “On the differentiability of functions and summability of trigonometric series,” Fund. Math.,26, 1–43 (1936).Google Scholar
  6. 6.
    Yu. B. Germeier, “Derivatives of Riemann and Vallée Poussin and their application to problems from the theory of trigonometric series,” Candidate's Dissertation, Physical-Mathematical Sciences, Moscow (1946).Google Scholar
  7. 7.
    I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], GITTL, Moscow (1950).Google Scholar
  8. 8.
    P. L. Ul'yanov, “Solved and unsolved problems of the theory of trigonometric and orthogonal series,” Usp. Mat. Nauk.,19, No. 1, 3–69 (1964).Google Scholar
  9. 9.
    W. Darsow, “On boundedness of trigonometric series,” J. Lond. Math. Soc.,35, No. 2(138), 237–238 (1960).Google Scholar
  10. 10.
    D. E. Men'shov, “On convergence in measure of trigonometric series,” Tr. Mat. Inst., Akad. Nauk SSSR,32, 3–97 (1950).Google Scholar
  11. 11.
    A. A. Talalyan, “Trigonometric series which are universal with respect to subseries,” Izv. Akad. Nauk SSSR, Ser. Mat.,27, No. 3, 621–660 (1963).Google Scholar
  12. 12.
    D. E. Men'shov, “On limits of indeterminacy with respect to measure of partial sums of trigonometric series,” Mat. Sb.,34, No. 3, 557–574 (1954).Google Scholar
  13. 13.
    A. A. Talalyanand F. G. Artuyunyan, “On convergence of a series in a Haar system to +∞,” Mat. Sb.,66, No. 2 (1965).Google Scholar
  14. 14.
    R. F. Gundy, “Martingale theory and pointwise convergence of certain orthogonal series,” Trans. Am. Math. Soc.,124, No. 2, 228–248 (1966).Google Scholar
  15. 15.
    V. A. Skvortsov, “Differentiation with respect to nets, and Haar series,” Mat. Zametki,4, No. 1, 33–40 (1968).Google Scholar
  16. 16.
    A. A. Talalyan, “Questions of representation and uniqueness in the theory of orthogonal series,” in: Mathematical Analysis, 1970 [in Russian], Moscow (1971), pp. 5–64.Google Scholar
  17. 17.
    R. I. Ovsepyan and A. A. Talalyan, “On convergence of orthogonal series to +∞,” Mat. Zametki,8, No. 2, 129–135 (1970).Google Scholar
  18. 18.
    P. L. Ul'yanov, “On convergence of orthgonal series to +∞,” Nauchnye Dokl. Vysshei Shkoly, Fiz.-Mat. Nauki, No. 4, 63–67 (1958).Google Scholar
  19. 19.
    N. E. Nörlund, Vorlesungen uber Differenzrechnung, Berlin (1924).Google Scholar
  20. 20.
    S. Saks, Theory of the Integral [Russian translation], Moscow (1949).Google Scholar
  21. 21.
    J.-P. Kahane and Y. Katznelson, “Sur les coefficients des séries de Fourier dont les sommes partielles sont positives sur un ensemble,” Stud. Math.,44, No. 6, 555–562 (1972).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • S. V. Konyagin
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR

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