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A relation between Nörlund and Abel summabilities

Author: Mehmet A. Sarıgöl
Journal: Proc. Amer. Math. Soc. 122 (1994), 223-225
MSC: Primary 40G05; Secondary 40D20, 40G10
MathSciNet review: 1254852
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Abstract: This paper gives a necessary and sufficient condition in order that every series summable by a Nörlund method with $ {p_n} = o({P_n})$ as $ n \to \infty $ should be summable by Abel's method to the same sum and so extends two theorems of Zygmund.

References [Enhancements On Off] (What's this?)

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  • [2] K. Knopp, Theory and application of infinite series, Blackie and Son, London and Glasgow, 1944.
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  • [5] A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776

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Article copyright: © Copyright 1994 American Mathematical Society