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On the converse of absolute Abel summability

Published online by Cambridge University Press:  24 October 2008

B. Kwee
Affiliation:
University of Malaya, Kuala Lumpur

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
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

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