On distributional finite hankel transform

Abstract

A new characterization of the finite Hankel transform for the generalized functions is developed, using families of regular generalized functions generated by smooth functions of slow growth. An inversion formula is established, in the distributional sense, using the new characterization. This new characterization is equivalent to Zemanian's extension of the Hankel transform to distributions obtained from the generalization of the Parseval's equation. © 1986, Taylor & Francis Group, LLC. All rights reserved.