Abstract
In this paper we generalize a result due to Hardy. We present a simple example of an everywhere divergent trigonometric series over the squares of the positive integers with coefficients which tend to zero.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
G. Freud, “Über trigonometrische Approximation und Fouriersche Reichen,” Math. Z.,78, 252–262 (1962).
Xie Ting-fan, “On lacunary Fourier series,” Referat. Zh., 1B, 102 (1966).
G. H. Hardy, “Weierstrass's nondifferentiable function,” Trans. Amer. Math. Soc.,17, 301–332 (1916).
N. K. Bary, A Treatise on Trigonometric Series, Vols.1 and 2, Macmillan, New York (1964).
A. Zygmund, Trigonometrical Series, Dover, New York (1955).
H. Steinhaus, “A divergent trigonometrical series,” J. London Math. Soc.,4, 86–88 (1929).
A. S. Belov, “Everywhere divergent trigonometrical series,” Matem. Sb.,85, No. 2, 224–237 (1971).
G. H. Hardy and J. E. Littlewood, “Some problems of diophantine approximation,” Proc. Nat. Acad. Sci.,2, 583–585 (1916).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 13, No. 4, pp. 481–492, April, 1973.
Rights and permissions
About this article
Cite this article
Belov, A.S. Study of some trigonometric series. Mathematical Notes of the Academy of Sciences of the USSR 13, 291–298 (1973). https://doi.org/10.1007/BF01146561
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01146561