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Summation of the integral conjugate to the Fourier integral of finite type

Published online by Cambridge University Press:  24 October 2008

Margaret Eleanor Grimshaw
Margaret Eleanor Grimshaw
Affiliation:
Newnham College
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Extract

1. The complete Denjoy-Fourier integral is of the form

where

the generating function ƒ(t) being integrable in the general Denjoy sense in every finite interval, and the integrals (1·2) being interpreted as principal values or in some other suitable way.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 23 , Issue 8 , October 1927 , pp. 871 - 881
Copyright
Copyright © Cambridge Philosophical Society 1927

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References

REFERENCES

1.Hardy, and Littlewood, , “The Allied Series of a Fourier Series.” Proc. London Math. Soc. (2), 24 (1925), 211–246.Google Scholar
2.Titchmarsh, E. C., “Conjugate Trigonometrical Integrals.” Proc. London Math. Soc. (2), 24 (1925), 109–130.Google Scholar