Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-05-01T14:32:40.972Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimal Rates of Summability

Published online by Cambridge University Press:  20 November 2018

J. A. Fridy
J. A. Fridy*
Affiliation:
Kent State University, Kent, Ohio
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.

During the early nineteenth century much effort was spent on attempts to find a “universal comparison test“: i.e., a sequence in l1 that dominates every other member of l1. The nonexistence of such a series converging at a minimal rate was demonstrated by Abel, et al. [1; 4; 7; 9, pp. 298-304].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 4 , 01 August 1978 , pp. 808 - 816
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Abel, N. H., J. f. d. reine u. angew. Math. 3 (1828), 79–82.Google Scholar
2. Dawson, D. F., On certain sequence-to-sequence transformations which preserve convergence, Proc. Amer. Math. Soc. 14 (1963), 542–545.Google Scholar
3. Dawson, D. F., Some rate invariant sequence transformations, Proc. Amer. Math. Soc. 15 (1964), 710–714.Google Scholar
4. Dini, U., Suite série a termini positivi, Annali Univ. Toscana 9 (1887), 5. Fridy, J. A., A note on absolute summability, Proc. Amer. Math. Soc. 20 (1969), 285–286.Google Scholar
6. Dini, U., Mercerian-type theorems for absolute summability, Port. Math. 33 (1974), 141–145.Google Scholar
7. Hadamard, J., Acta Mathematica 18 (1894), 319–336.Google Scholar
8. Hardy, G. H., Divergent series (Clarendon Press, Oxford, 1949).Google Scholar
9. Knopp, K., Theory and application of infinite series (Blackie & Son Limited, Glasgow, 1928).Google Scholar
10. Knopp, K. and Lorentz, G. G., Beitrdge zur absoluten Limitierung Arch. Math. 2 (1949), 10–16.Google Scholar
11. Powell, R. E. and Shah, S. M., Summability theory and its applications (Van Nostrand Reinhold Co., London, 1972).Google Scholar
12. Wilansky, A., Functional analysis (Blaisdell, New York, 1964).Google Scholar