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The Resultant of Two Fourier Kernels

Published online by Cambridge University Press:  24 October 2008

G. H. Hardy
G. H. Hardy
Affiliation:
Trinity College
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Extract

1. A “Fourier kernel” means here a function K(x) which gives rise to a formula

of the Fourier type. Thus

are Fourier kernels. If K(x) is a Fourier kernel, λ is real, and a positive, then

are Fourier kernels.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 31 , Issue 1 , January 1935 , pp. 1 - 6
Copyright
Copyright © Cambridge Philosophical Society 1935

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References

REFERENCES

(1)Hardy, G. H., “Notes on some points in the integral calculus (LXIII)”, Messenger of Math. 56 (1927), 186–92.Google Scholar
(2)Hardy, G. H. and Titchmarsh, E. C., “A class of Fourier kernels”, Proc. London Math. Soc. (2), 35 (1933), 116–55.CrossRefGoogle Scholar
(3)Plancherel, M., “Sur les formules de réciprocité du type de Fourier”, Journal London Math. Soc. 8 (1933), 220–26.Google Scholar
(4)Titchmarsh, E. C., “A proof of a theorem of Watson”, Journal London Math. Soc. 8 (1933), 217–20.CrossRefGoogle Scholar
(5)Watson, G. N., Theory of Bessel functions, Cambridge, 1922.Google Scholar
(6)Watson, G. N., “General transforms”, Proc. London Math. Soc. (2), 35 (1933), 156–99.Google Scholar