On Hankel transform

Duran, Antonio J.

doi:10.1090/S0002-9939-1990-1019749-9

On Hankel transform
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by Antonio J. Duran PDF

Proc. Amer. Math. Soc. 110 (1990), 417-424 Request permission

Abstract:

In this paper, using some results of the author on Hankel transform in the Schwartz and Gel’fand-Shilov spaces, we characterize the integral operators of Hankel type which are isomorphisms between the spaces ${H_\mu }$ of Zemanian. As a particular case, we obtain the classical Zemanian results on Hankel transform, some results of Mendez, and improve some results of Lee. Finally, we use these results to characterize the functions $f$ of the Schwartz space which satisfy $\smallint _0^\infty {t^{\alpha + n}}f(t)dt = 0$ for all $n \geq 0$ and $\alpha > - 1$.

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Generalized integral transformations