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Proceedings of the American Mathematical Society

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

 

 

Logarithmic means and summability by the circle methods


Author: M. R. Parameswaran
Journal: Proc. Amer. Math. Soc. 52 (1975), 279-282
MSC: Primary 40G10
DOI: https://doi.org/10.1090/S0002-9939-1975-0387883-4
MathSciNet review: 0387883
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Abstract: It is proved that if the logarithmic means of a sequence $ \{ {s_n}\} $ satisfy a certain order condition then the sequence $ \{ {s_n}\} $ will be summable by every circle method (Kreisverfahren) stronger than convergence; the condition is shown to be a best possible one, for even summability by the collective circle method. A second set of conditions leading to the conclusion of summability by every circle method is also proved.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0387883-4
Keywords: Logarithmic means, summability, circle methods
Article copyright: © Copyright 1975 American Mathematical Society