Generalized hankel-type transformation for a class of tempered ultradistributions of roumieu-type

Abstract EN

As the third in a series of papers the present paper aims at investigating a theory supporting Henkel-type transformation on certain spaces of generalized functions.

In an attempt to extend the transform to a space of generalized functions, namely, a space of tempered ultra-distributions, adequate definitions of classes of rapid descent ultra-differentiable functions is provided.

In light of those definitions, various mappings involving various differential operators are shown to be continuous.

Further, the generalized Henkel-type transform of Roomie-type tempered (of slow growth) ultra-distributions is obtained.