Distributional Watson Transforms
Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1191-1197
Voir la notice de l'article provenant de la source Cambridge University Press
All our notation is as denned in [2] with the restriction to n = 1. However, for our purposes, we introduce a sequence of norms by in It is not difficult to see that turns out to be a fundamental space.It is a well-known fact that the Watson transform and the Mellin transform are connected by the fact that and if and only if K(s)K(l — s) = 1, where K(s) is the Mellin transform of k(x). Further, the Hankel transform and Hilbert transform can be considered as special cases of Watson transforms.
Hsu, Hsing-Yuan. Distributional Watson Transforms. Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1191-1197. doi: 10.4153/CJM-1972-129-5
@article{10_4153_CJM_1972_129_5,
author = {Hsu, Hsing-Yuan},
title = {Distributional {Watson} {Transforms}},
journal = {Canadian journal of mathematics},
pages = {1191--1197},
year = {1972},
volume = {24},
number = {6},
doi = {10.4153/CJM-1972-129-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-129-5/}
}
[1] 1. Titchmarsch, E. C., Introduction to the theory of Fourier integrals. 2nd edition (Oxford University Press, 1948). Google Scholar
[2] 2. Zemanian, A., The distributional Laplace and Mellin transformations, SI AM J. Appl. Math. 14 (1966), 41–59. Google Scholar
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