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An O-Tauberian theorem and a high indices theorem for power series methods of summability*

Published online by Cambridge University Press:  24 October 2008

David Borwein  and
Werner Kratz
David Borwein
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario, CanadaN6A 557
Werner Kratz
Affiliation:
Abteilung Mathematik, Universität Ulm, Helmholtzstr. 18, D-7900 Ulm/Donau, Germany
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Abstract

We improve known Tauberian results concerning the power series method of summability Jp based on the sequence {pn} by removing the condition that pn be asymptotically logarithmico-exponential. We also prove an entirely new Tauberian result for rapidly decreasing pn.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 2 , March 1994 , pp. 365 - 375
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

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