Distributional Watson Transforms

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Abstract
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.

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