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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Power series methods of summability: positivity and gap perfectness


Authors: A. Jakimovski, W. Meyer-König and K. Zeller
Journal: Trans. Amer. Math. Soc. 266 (1981), 309-317
MSC: Primary 40H05; Secondary 40G10
MathSciNet review: 613798
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Abstract: A class of power series methods of summability is defined. By means of a positivity argument (Bohman-Korovkin) it is shown that each method of the class is gap perfect. This fact facilitates the proof of Tauberian gap theorems. Several examples are given.


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DOI: https://doi.org/10.1090/S0002-9947-1981-0613798-7
Keywords: Power series methods of summability, positivity, gap perfectness, Tauberian gap theorems, generalized Abel methods of summability, logarithmic method of summability
Article copyright: © Copyright 1981 American Mathematical Society