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On Hankel transform

Author: Antonio J. Duran
Journal: Proc. Amer. Math. Soc. 110 (1990), 417-424
MSC: Primary 46F12; Secondary 44A15, 47G05
MathSciNet review: 1019749
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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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Keywords: Hankel transform, Gel'fand Shilov spaces, Lee spaces
Article copyright: © Copyright 1990 American Mathematical Society

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