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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A Tauberian theorem for Hausdorff methods


Authors: Brian Kuttner and Mangalam R. Parameswaran
Journal: Proc. Amer. Math. Soc. 102 (1988), 139-144
MSC: Primary 40G05,; Secondary 40E05
MathSciNet review: 915732
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0915732-0
PII: S 0002-9939(1988)0915732-0
Article copyright: © Copyright 1988 American Mathematical Society