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On Young's criteria for the convergence of Fourier series and their conjugates

Published online by Cambridge University Press:  24 October 2008

W. L. C. Sargent
W. L. C. Sargent
Affiliation:
Newnham College
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Extract

1. Young's criterion for the convergence of a Fourier series may be stated in the following form:

The integral

tends to zero as ω → ∞ whenever

(A) ø(t) is absolutely integrable in (0, a),

(B) ø(t) → 0 in mean as t → 0,

(C) tø(t) is of bounded variation to the immediate right of t = 0 and, as t → 0,

Type
Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 1 , January 1929 , pp. 26 - 30
Copyright
Copyright © Cambridge Philosophical Society 1929

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References

REFERENCES

1.Hardy, G. H. and Littlewood, J. E., Math. Zeitschrift, vol. XIX (1923), 67–96.Google Scholar
2.Hardy, G. H. and Littlewood, J. E., Proc. London Math. Soc., (2) vol. XXVIII (1928), 301–311.CrossRefGoogle Scholar
3.S., Pollard, Journal London Math. Soc., vol. II (1927), 255–262.Google Scholar