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Notes on special systems of orthogonal functions (IV): the orthogonal functions of whittaker's cardinal series

Published online by Cambridge University Press:  24 October 2008

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

Suppose that n runs through all integral values, that (øn) is a system of normal orthogonal functions for the interval (−∞, ∞), and that ψn is the Fourier transform of øn. Then, by Parseval's theorem for Fourier transforms,

and (ψn) is also a normal orthogonal system.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 37 , Issue 4 , October 1941 , pp. 331 - 348
Copyright
Copyright © Cambridge Philosophical Society 1941

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References

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