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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Logarithmic means and summability by the circle methods
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by M. R. Parameswaran PDF
Proc. Amer. Math. Soc. 52 (1975), 279-282 Request permission

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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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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