This is a preview of subscription content, log in via an institution to check access.
Literature Cited
A. S. Belov, “On the sum of a lacunary series,” Tr. Mosk. Mat. Obshch.,33, 107–153 (1975).
G. H. Hardy, “Weierstrass's nondifferentiable function,” Trans. Am. Math. Soc.,17, 301–325 (1916).
G. Freud, “Über trigonometrische Approximation und Fouriersche Reihen,” Math. Z.,78, 252–262 (1962).
G. Freud, “On Fourier series with Hadamard gaps,” Stud. Sci. Math. Hung.,1, 87–96 (1966).
Xie Ting-fan, “On lacunary Fourier series,” Chinese Math.,5, 340–345 (1964).
J.-P. Kahane, “Lacunary Taylor and Fourier series,” Bull. Am. Math. Soc.,70, 199–213 (1964).
A. I. Rubinshtein, “On coefficients of lacunary series,” Vestn. Mosk. Gos. Univ., Ser. Mat., No. 3, 48–57 (1966).
M. Izumi and S. Izumi, “On lacunary Fourier series,” Proc. Jpn. Acad.,41, 648–651 (1965).
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).
A. S. Belov, “On the Sidon-Zygmund inequality in the theory of lacunary trigonometric series,” Mat. Zametki,30, No. 4, 501–515 (1981).
A. S. Belov, “Quasianalyticity of the sum of a lacunary series,” Mat. Sb.,99, 433–467 (1976).
Additional information
Ivanovo. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 28, No. 5, pp. 32–41, September–October, 1987.
Rights and permissions
About this article
Cite this article
Belov, A.S. Smoothness of the sum of a lacunary trigonometric series. Sib Math J 28, 717–724 (1987). https://doi.org/10.1007/BF00969310
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00969310