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The Absolute Summability (A) of Fourier Series

Published online by Cambridge University Press:  20 January 2009

L. S. Bosanquet
L. S. Bosanquet
Affiliation:
University College, London.
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Sufficient conditions for the absolute summability (A)1 of a Fourier series have been given by J. M. Whittaker and B. N. Prasad. They obtained theorem 1 below in the cases α = 0 and α = 1 respectively. Theorem 1 is contained in theorem 2, which was given by Prasad in the case α = 0.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 4 , Issue 1 , March 1934 , pp. 13 - 17
Copyright
Copyright © Edinburgh Mathematical Society 1934

References

REFERENCES

1.Bosanquet, L. S.. “The Cesàro summation of Fourier series and allied series.” Proc. London Math. Soc. In the press.Google Scholar
2.Prasad, B. N.. “The Absolute Summability (A) of Fourier series.” Proc. Edin-burgh Math. Soc. (2) 2 (1930–1931) 129–134.CrossRefGoogle Scholar
3.Prasad, B. N.. “On the summability of Fourier series and the bounded variation of power series.” Proc. London Math. Soc. (2), 35 (1933), 407–424.CrossRefGoogle Scholar
4.Whittaker, J. M.. “The Absolute Summability of Fourier series.” Proc. Edin-burgh Math. Soc. (2) 2 (1930–1931) 1–5.CrossRefGoogle Scholar