Literature cited
K. Weierstrass, Abhandlungen aus der Funktionenlehre, Berlin (1886), pp. 97–101.
G. H. Hardy, “Weierstrass's nondifferentiable function,” Trans. Am. Math. Soc.,17, No. 3, 301–325 (1916).
S. Itatsu, “Differentiability of Riemann's function,” Proc. Jpn. Acad.,A57, No. 10, 492–495 (1981).
A. Zygmund, “Smooth functions,” Duke Math. J.,12, No. 1, 47–76 (1945).
M. Weiss, “The law of the iterated logarithm for lacunary trigonometric series,” Trans. Am. Math. Soc.,91, No. 3, 531–555 (1959).
R. Salen and A. Zygmund, “On lacunary trigonometric series,” Proc. Nat. Acad. Sci. USA,33, 333–348 (1947);34, 54–62 (1948).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 36, No. 1, pp. 35–38, July, 1984.
The author expresses sincere gratitude to Yu. V. Prokhorov for support and helpful discussions.
Rights and permissions
About this article
Cite this article
Gamkrelidze, N.G. Modulus of continuity of the Weierstrass function. Mathematical Notes of the Academy of Sciences of the USSR 36, 510–512 (1984). https://doi.org/10.1007/BF01139550
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01139550