Hankel transformation of Colombeau type tempered generalized functions
The Hankel transformation is defined on a new class \({\mathcal H}_{\mu,\tau}\) of generalized functions of Colombeau type. The space of distributions of slow growth \({\mathcal H}_\mu\) introduced by Zemanian to define the Hankel transformation is contained in \({\mathcal H}_{\mu,\tau}\). Moreover, the introduced Hankel transformation on \({\mathcal H}_{\mu,\tau}\) coincides in a suitable weak sense with the one defined by Zemanian when restricted on the Zemanian slow growth distributions. Some properties of the Hankel transformation as well as the Hankel translation and Hankel convolution on the space \({\mathcal H}_{\mu,\tau}\) are given.
scientific article; zbMATH DE number 1115471