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 $A \cdot {C_\alpha }(\alpha {\text { > }} - 1)$.References
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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