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On the converse of absolute Abel summability
Published online by Cambridge University Press: 24 October 2008
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