A criterion for the (e, c)-summability of Fourier series
Published online by Cambridge University Press: 24 October 2008
Extract
1. A series with partial sums {An} is said to be summable (e, c) (c > 0) if
exists, where it is to be understood that An+k = 0 when n+k < 0. The (e, c)-sum-mability method which is a regular method of summation was introduced by Hardy and Littlewood (3) (cf. also (5)) as an auxiliary method to prove the Tauberian theorem for Borel summability, viz, if Σan is summable (B) to A and an = 0(n−½), then it converges to A.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 1 , July 1982 , pp. 121 - 127
- Copyright
- Copyright © Cambridge Philosophical Society 1982
References
REFERENCES
- 1
- Cited by