Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-22T05:39:44.779Z Has data issue: false hasContentIssue false
  • English
  • Français

Translativity for Strong Borel Summability

Published online by Cambridge University Press:  20 November 2018

Lee Lorch
Lee Lorch*
Affiliation:
Summer Research Institute, Canadian Mathematical Congress, University of Alberta, Edmonton, Alberta
Rights & Permissions [Opens in a new window]

Extract

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 an obvious property of convergence that implies that sn+k exists and equals s for k = -1 (left translativity ) and for k = 1 (right translativity). Not so for sumrnability.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 5 , December 1966 , pp. 639 - 645
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Gaier, D., Zur Frage der Indexverschiebung beim Borel-Verfahren, Math. Zeitschr. vol. 58 (1953), pages 453-455.Google Scholar
2. Garten, V., Űber den Einfluss endlich vieler Anderungen auf das Borelsche Limitierungsverfahren. Math. Zeitschr. vol. 40 (1936), pages 756-759.Google Scholar
3. Hardy, G. H., Divergent Series. (1949).Google Scholar
4. Karamata, J., Űber die Indexverschiebung beim Borelschen Limitierungsverfahren. Math. Zeitschr., vol. 45 (1939), pages 635-641.Google Scholar
5. Polya, G., Űber die kleinsten ganzen Funktionen, der en samtliche Derivierten im Punkte z=0 ganzzahlig sind. Tohoku Mathematical Journal, vol. 19 (1921), pages 65-69.Google Scholar
6. Szász, O., On the product of two summability methods. Ann. Soc. Polon. Math. vol. 25 (1952), pages 75-84.Google Scholar
7. Widder, D.V., Advanced Calculus. 2d. éd., (1961).Google Scholar

An addendum has been issued for this article:

Addendum