Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T13:18:36.798Z Has data issue: false hasContentIssue false
  • English
  • Français

A Tauberian theorem for Borel summability

Published online by Cambridge University Press:  24 October 2008

B. Kuttner  and
M. R. Parameswaran
B. Kuttner
Affiliation:
University of Birmingham, Birmingham B15 2TT
M. R. Parameswaran
Affiliation:
University of Manitoba, Winnipeg, Manitoba, CanadaR3T 2N2
Get access Rights & Permissions [Opens in a new window]

Extract

1. We use Eα to denote the Euler transformation obtained as the special case of the Hausdorff transformation (H, μn) in which μn = αn (see [5], §§64, 72; in the notation of Hardy's book [1], our Eα is (E, q) with q = (1 − α)/α). Eα is regular if and only if 0 < α < 1, and in this range Eα increases in strength as α decreases since EαEβ = Eαβ. Also, E1 = I, the identity transformation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 1 , July 1987 , pp. 135 - 138
Copyright
Copyright © Cambridge Philosophical Society 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Hardy, G. H.. Divergent Series (Clarendon Press, Oxford, 1949).Google Scholar
[2] Amir, Amnon (Jakimovski). Some relations between the methods of summability of Abel, Borel Cesàro, Hölder and Hausdorff. J. d'Analyse Math. 3 (1953/1954), 346–381.CrossRefGoogle Scholar
[3] Meyer-König, W.. Untersuchungen über einige verwandte Limitierungsverfahren. Math. Zeit. 52 (1949), 257–304.CrossRefGoogle Scholar
[4] Parameswaran, M. R.. On a generalization of a theorem of Meyer-König. Math. Zeit. 162 (1978), 201–204.CrossRefGoogle Scholar
[5] Zeller, K. and Beekman, W.. Theorieder Limitierungsverfahren (Springer-Verlag, 1970).CrossRefGoogle Scholar