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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
Affiliation:
Trinity CollegeCambridge

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.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1941

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References

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