Abstract
Necessary and sufficient conditions are derived for the convergence of a trigonometric series to a function of bounded variation on the interval (α, β) ⊂[-π, π]. For the case in which the coefficients satisfy certain conditions, the continuity of the sum function is investigated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
A. Zygmund, Trigonometric Series, Vol. 1, Cambridge Univ. Press, New York (1959).
G. Goes, “Lokale Konvergenzbedingungen für trigonometrische Reihen und für Potenzreihen,” Math. Z.,82, 389–393 (1963).
S. Sidon, “Über die Fourierkoeffizienteneiner stetigen Funktion von beschränkter Schwankung,” Acta Sci. Math.,2, 43–46 (1924).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 8, No. 1, pp. 47–58, July, 1970.
The author wishes to thank his scientific supervisor S. A. Telyakovskii for suggesting this problem and for his interest in the work.
Rights and permissions
About this article
Cite this article
Oskolkov, K.I. The convergence of trigonometric series to functions of bounded variation. Mathematical Notes of the Academy of Sciences of the USSR 8, 496–503 (1970). https://doi.org/10.1007/BF01093441
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01093441