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A note on repeated general transformations

Published online by Cambridge University Press:  24 October 2008

A. P. Guinand
A. P. Guinand
Affiliation:
Military College of ScienceShrivenham
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Abstract

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Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 2 , April 1950 , pp. 354 - 355
Copyright
Copyright © Cambridge Philosophical Society 1950

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References

* This is a straightforward extension of Watson's results for functions of a single variable. Cf. Titchmarsh, E. C., Fourier integrals (Oxford, 1937)Google Scholar, Chapter viii.

† The integral (2) does not converge for a function satisfying condition (i) unless it is almost everywhere zero. However, the rule applies to functions such as (x + y)−1, which is accordingly self-reciprocal for all transformations of the type described.