GENERALIZED HANKEL-TYPE TRANSFORMATION FOR A CLASS OF TEMPERED ULTRADISTRIBUTIONS OF ROUMIEU-TYPE

As the third in a series of papers the present paper aims at investigating a theory supporting Hankel-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 ultradistributions, an adequate definitions of classes of rapid descent ultradifferentiable functions is provided. In light of those definitions, various mappings involving various differential operators are shown to be continuous. Further, the generalized Hankel-type transform of Roumieu-type tempered (of slow growth) ultradistributions is obtained.