On an Inversion Operator for the Fourier Transformation
Canadian mathematical bulletin, Tome 3 (1960) no. 2, pp. 157-165
Voir la notice de l'article provenant de la source Cambridge University Press
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
Rooney, P. G. On an Inversion Operator for the Fourier Transformation. Canadian mathematical bulletin, Tome 3 (1960) no. 2, pp. 157-165. doi: 10.4153/CMB-1960-020-x
@article{10_4153_CMB_1960_020_x,
author = {Rooney, P. G.},
title = {On an {Inversion} {Operator} for the {Fourier} {Transformation}},
journal = {Canadian mathematical bulletin},
pages = {157--165},
year = {1960},
volume = {3},
number = {2},
doi = {10.4153/CMB-1960-020-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1960-020-x/}
}
[1] 1. Rooney, P. G., On the representation of functions as Fourier transforms, Canad. J. Math. 11 (1959), 168-174.10.4153/CJM-1959-022-7 Google Scholar
[2] 2. Rooney, P. G., On the inversion of general transformations, Canad. Math. Bull. 2 (1959), 19-24.10.4153/CMB-1959-005-3 Google Scholar
[3] 3. Titchmarsh, E. C., The Theory of Functions, 2nd edition (Oxford, 1939). Google Scholar
[4] 4. Titchmarsh, E. C., The Theory of Fourier Integrals, 2nd edition (Oxford, 1948). Google Scholar
[5] 5. Widder, D. V., The Laplace Transform (Princeton, 1941). Google Scholar
Cité par Sources :