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

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A Tauberian theorem for Hausdorff methods
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by Brian Kuttner and Mangalam R. Parameswaran PDF
Proc. Amer. Math. Soc. 102 (1988), 139-144 Request permission

Abstract:

Let $H = (H,\chi )$ be a regular Hausdorff summability method defined by the function $\chi \in {\text {BV}}\left [ {0,1} \right ]$. It is shown that if $\chi$ is absolutely continuous on $\left [ {0,1} \right ]$, then the methods $H$ and $V \cdot H$ are equivalent for bounded sequences, where $V$ belongs to a certain class of summability methods which includes the Cesàro methods ${C_\alpha }(\alpha {\text { > }}0)$, the Abel method $A$, and the methods $A \cdot {C_\alpha }(\alpha {\text { > }} - 1)$.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 102 (1988), 139-144
  • MSC: Primary 40G05,; Secondary 40E05
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0915732-0
  • MathSciNet review: 915732