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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Summability factors for Cesàro methods
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by David F. Dawson
Proc. Amer. Math. Soc. 73 (1979), 371-374
DOI: https://doi.org/10.1090/S0002-9939-1979-0518523-2
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Abstract:

It is shown that if each of r and s is a nonnegative integer and $\{ {f_p}\}$ is a complex sequence such that $\Sigma {f_p}{a_p}$ is Cesàro summable of order s whenever $\Sigma {a_p}$ is Cesàro summable of order r, then $\Sigma {f_p}{a_p}$ is Cesàro summable of order r whenever $\Sigma {a_p}$ is Cesàro summable of order r.
References
  • David F. Dawson, A generalization of a theorem of Hans Hahn concerning matrix summability, Boll. Un. Mat. Ital. (4) 3 (1970), 349–356. MR 0265813
    • Tetsuzo Kojima, On generalized Toeplitz’s theorems on limit and their applications, Tôhoku Math. J. 12 (1917), 291-326.
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Bibliographic Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 73 (1979), 371-374
  • MSC: Primary 40G05
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0518523-2
  • MathSciNet review: 518523