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On Cesàro and Abel Summability Factors for Integrals

Published online by Cambridge University Press:  20 November 2018

David Borwein  and
Brian Thorpe
David Borwein
Affiliation:
The University of Western Ontario, London, Ontario
Brian Thorpe
Affiliation:
The University of Birmingham, Birmingham, England
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Many results have been obtained about factors transforming integrals summable by ordinary and absolute Cesàro methods of non-negative orders into integrals summable by such methods (see [4], [2], [6], [3]) and also into integrals summable by the ordinary and absolute Abel methods (see [7]). Since the Cesàro summability methods (C, α) and |C, α| for integrals are defined for α ≦ –1, it is natural to try to extend the above mentioned results for α ≦ 0 to the case –1 ≧ α < 0. In this paper we restrict attention to the simplest case α = –1, and classify the summability factors from (C, –1) and |C, –1| to (C, –1) , |C, –1|, (C, λ), |C, λ|, A and |A|, where λ ≦ 0 and A denotes Abel summability.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 2 , 01 April 1986 , pp. 453 - 477
Copyright
Copyright © Canadian Mathematical Society 1986

References

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