Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620
  • [2] K. Knopp, Theory and application of infinite series, Blackie and Son, London and Glasgow, 1944.
  • [3] Gordon M. Petersen, Regular matrix transformations, McGraw-Hill Publishing Co., Ltd., London-New York-Toronto, Ont., 1966. MR 0225045
  • [4] A. Peyerimhoff, Lectures on summability, Lecture Notes in Mathematics, Vol. 107, Springer-Verlag, Berlin-New York, 1969. MR 0463744
  • [5] A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 40G05, 40D20, 40G10

Retrieve articles in all journals with MSC: 40G05, 40D20, 40G10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1254852-3
Article copyright: © Copyright 1994 American Mathematical Society