On Hankel transform

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 μ {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 f of the Schwartz space which satisfy ∫ 0 ∞ t α + n f ( t ) d t = 0 \smallint _0^\infty {t^{\alpha + n}}f(t)dt = 0 for all n ≥ 0 n \geq 0 and α > − 1 \alpha > - 1 .