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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

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