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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
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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

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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