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A criterion for the (e, c)-summability of Fourier series

Published online by Cambridge University Press:  24 October 2008

Jamil A. Siddiqi
Jamil A. Siddiqi
Affiliation:
Laval University, Quebec
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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

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References

REFERENCES

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