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Gap Tauberian theorem for generalized Abel summability

Published online by Cambridge University Press:  24 October 2008

V. K. Krishnan
V. K. Krishnan
Affiliation:
St Thomas College, Trichur, India
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Extract

Let α > − 1. For a given series write

it being tacitly assumed that the series defining a(t) and A(t) converge for all t > 0. Σan is said to be summable (Aα) to A if

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 3 , November 1975 , pp. 497 - 500
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Borwein, D.On a scale of Abel-type summability methods. Proc. Cambridge Philos. Soc. 53 (1957), 319–322.CrossRefGoogle Scholar
(2)Hardy, G. H.Divergent series (Oxford, 1949).Google Scholar
(3)Pitt, H. R.Tauberian theorems (Tata Institute Monographs No. 2, Bombay, 1958).Google Scholar