Siberian Mathematical Journal

, Volume 28, Issue 5, pp 717–724 | Cite as

Smoothness of the sum of a lacunary trigonometric series

  • A. S. Belov


Trigonometric Series Lacunary Trigonometric Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    A. S. Belov, “On the sum of a lacunary series,” Tr. Mosk. Mat. Obshch.,33, 107–153 (1975).Google Scholar
  2. 2.
    G. H. Hardy, “Weierstrass's nondifferentiable function,” Trans. Am. Math. Soc.,17, 301–325 (1916).Google Scholar
  3. 3.
    G. Freud, “Über trigonometrische Approximation und Fouriersche Reihen,” Math. Z.,78, 252–262 (1962).Google Scholar
  4. 4.
    G. Freud, “On Fourier series with Hadamard gaps,” Stud. Sci. Math. Hung.,1, 87–96 (1966).Google Scholar
  5. 5.
    Xie Ting-fan, “On lacunary Fourier series,” Chinese Math.,5, 340–345 (1964).Google Scholar
  6. 6.
    J.-P. Kahane, “Lacunary Taylor and Fourier series,” Bull. Am. Math. Soc.,70, 199–213 (1964).Google Scholar
  7. 7.
    A. I. Rubinshtein, “On coefficients of lacunary series,” Vestn. Mosk. Gos. Univ., Ser. Mat., No. 3, 48–57 (1966).Google Scholar
  8. 8.
    M. Izumi and S. Izumi, “On lacunary Fourier series,” Proc. Jpn. Acad.,41, 648–651 (1965).Google Scholar
  9. 9.
    A. S. Belov, “Some properties of trigonometric series,” Author's Abstract of Candidate's Dissertation, Physical-Mathematical Sciences, V. A. Steklov Inst. of Math., Academy of Sciences of the USSR, Moscow (1976).Google Scholar
  10. 10.
    A. S. Belov, “On the Sidon-Zygmund inequality in the theory of lacunary trigonometric series,” Mat. Zametki,30, No. 4, 501–515 (1981).Google Scholar
  11. 11.
    A. S. Belov, “Quasianalyticity of the sum of a lacunary series,” Mat. Sb.,99, 433–467 (1976).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • A. S. Belov

There are no affiliations available

Personalised recommendations