A relation between Nörlund and Abel summabilities
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- by Mehmet A. Sarıgöl PDF
- Proc. Amer. Math. Soc. 122 (1994), 223-225 Request permission
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
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- Gordon M. Petersen, Regular matrix transformations, McGraw-Hill Publishing Co., Ltd., London-New York-Toronto, Ont., 1966. MR 0225045
- A. Peyerimhoff, Lectures on summability, Lecture Notes in Mathematics, Vol. 107, Springer-Verlag, Berlin-New York, 1969. MR 0463744, DOI 10.1007/BFb0060951
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 223-225
- MSC: Primary 40G05; Secondary 40D20, 40G10
- DOI: https://doi.org/10.1090/S0002-9939-1994-1254852-3
- MathSciNet review: 1254852