The distributional hankel transform, its inversion and application

Abstract

W.Y.Lee extended A.L.Schwartz's Hankel transform to distributions and posed four open problems. We solve these problems and modify his main result that the Schwartz's Hankel transform is a continuous linear mapping from Fμinto Gμ We show that it is in fact an automorphism on Fμ Further, the Hankel transform due to Zemanian is extended for allμ in R

Keywords:

• Schwartz's Hankel transform of distributions
• test function spaces
• open mapping theorem

AMS(MOS)::

• 46F12
• 44A20
• 44A15