On some Whittaker transform of a special function kernel for a class of generalized functions

Abstract

An investigation has been carried out to studying extensions of Whittaker integral operators to classes of generalized functions. By conducting an approach, dissimilar to our previous works, we discuss a Whittaker transform whose kernel involved with Fox’s H-functions on classes of Boehmians which basically generalize distributions. However, despite changes in the kernel function, the Whittaker transform exists in its new configuration and attains many properties inherited from its classical integral. A convolution theorem of the Whittaker transform has also been derived to connect the new spaces.