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On the converse of absolute Abel summability

Published online by Cambridge University Press:  24 October 2008

B. Kwee
B. Kwee
Affiliation:
University of Malaya, Kuala Lumpur
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Extract

The series is said to be summable A to s if the power series converges to φ(x) for 0 ⋞ x < 1 and limx→1 φ(x) = s. If the function ⋞(x) is of bounded variation over the same interval, the series is said to be summable │A│. It is easy to prove │A│ ⊆ A, i.e. a series summable │A│ is necessarily summable A to the same sum.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 3 , May 1982 , pp. 453 - 456
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

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