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On an Inversion Operator for the Fourier Transformation

Published online by Cambridge University Press:  20 November 2018

P. G. Rooney
P. G. Rooney*
Affiliation:
University of Toronto
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In an earlier paper [1] we presented a representation theory for the Fourier transformation defined by

1.1

for functions f in certain function spaces. This theory made use of an operator

1.2

where k = 1, 2,…, and it was stated without proof that this operator is an inversion operator for the Fourier transformation; that is, that under certain conditions

1.3

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 3 , Issue 2 , 01 May 1960 , pp. 157 - 165
Copyright
Copyright © Canadian Mathematical Society 1960

References

1. Rooney, P. G., On the representation of functions as Fourier transforms, Canad. J. Math. 11 (1959), 168-174.10.4153/CJM-1959-022-7Google Scholar
2. Rooney, P. G., On the inversion of general transformations, Canad. Math. Bull. 2 (1959), 19-24.10.4153/CMB-1959-005-3Google Scholar
3. Titchmarsh, E. C., The Theory of Functions, 2nd edition (Oxford, 1939).Google Scholar
4. Titchmarsh, E. C., The Theory of Fourier Integrals, 2nd edition (Oxford, 1948).Google Scholar
5. Widder, D. V., The Laplace Transform (Princeton, 1941).Google Scholar