Article contents
A Tauberian Theorem Concerning Borel-Type and Riesz Summability Methods
Published online by Cambridge University Press: 20 November 2018
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
It is proved that the summability of a series by the Borel-type summability method (B,α,β) together with a certain Tauberian condition implies its summability by the Riesz method (R, log(n + l),p).
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1992
References
1.
Borwein, D., On methods of summability based on integral junctions II, Proc. Cambridge Phil. Soc. 56 (1960), 125–131.Google Scholar
2.
Borwein, D., Relations between Borel-type methods of summability, J. London Math. Soc. 35(1960),65–70.Google Scholar
3.
Borwein, D., A Tauberian theorem for Borel-type methods of summability, Canadian J. Math. 21(1969),740–747.Google Scholar
4.
Borwein, D. and I. Robinson, J. W., A Tauberian theorem for Borel-type methods of summability, J. Reine Angew. Math. 273(1975),153–164.Google Scholar
5.
Borwein, D. and Markovich, T., A Tauberian theorem concerning Borel-type and Cesàro methods of summability, Canadian J. Math. 40(1988),228–247.Google Scholar
7.
Kuttner, B., On iterated Riesz transforms of order 1, Proc. London Math. Soc. (3)29(1974),272–288.Google Scholar
8.
Kwee, B., On relations between Borel and Riesz methods of summation, Bull. London Math. Soc. 21(1989),387–393.Google Scholar
You have
Access
- 2
- Cited by