Notes for Hartley transforms of generalized functions

Abstract

The classical Hartley transform, originally introduced by Hartley as a real transform with a number of properties being similar to the properties of Fourier transform.  In this work, we extend the Hartley transform to certain space of distributions of compact support. Further, we establish that the Hartley transform and its inverse are one to one and onto mappings in the space of Boehmians.  Moreover, continuity with respect to δ and ∆ convergence is discussed in some detail.  Certain theorems are also proved.