Abstract
It is proved that if a series is absolute summable by a Cesàro (C,α) method, then it is summable (C,β) for anyβ, such that Reα = Reβ>−1.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
S. Baron, Introduction to the Theory of Summability of Series [in Russian], Tartu (1966).
I. I. Volkov, “The (C,α) summation of divergent series,” Trudy Mosk. In-ta Mekhanizatsii i Élektrifikatsii s. kh.,4, No. 1, 137–146 (1959).
I. I. Volkov, “Summability sets for Cesàro methods of complex order,” Uspekhi Matem. Nauk,17, No. 1, 161–168 (1962).
A. Zygmund, Trigonometric Series, Vol. 1, Cambridge University Press (1959).
H. Hahn, “Über Folgen Linearer Operationen,” Monatsh. Math. und Phys.,32, 3–88 (1922).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 9, No. 1, pp. 13–18, January, 1971.
Rights and permissions
About this article
Cite this article
Volkov, I.I. Relation between summability and absolute summability by Cesaro means of complex order. Mathematical Notes of the Academy of Sciences of the USSR 9, 9–11 (1971). https://doi.org/10.1007/BF01405042
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01405042