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

 

$ o$-but not $ O$-Tauberian theorems


Authors: G. G. Lorentz and K. L. Zeller
Journal: Proc. Amer. Math. Soc. 45 (1974), 401-404
MSC: Primary 40E05
MathSciNet review: 0346370
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Abstract: Let $ A$ be a regular matrix summability method. Relations between different Tauberian theorems for $ A$ are discussed. We show that most summability methods possess some $ o$-Tauberian theorem with the property that the corresponding $ O$-Tauberian theorem is not valid.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0346370-9
PII: S 0002-9939(1974)0346370-9
Article copyright: © Copyright 1974 American Mathematical Society