Convolution of Roumieu ultradistributions in sequential approach

Abstract

We consider several general sequential conditions for convolvability of two Roumieu ultradistributions and prove that they are equivalent to the convolvability of these ultradistributions in the sense of Pilipovic and Prangoski. The discussed conditions, based on two classes of approximate units and corresponding sequential conditions of integrability of Roumieu ultradistributions, are analogous to the known convolvability conditions in the space of distributions and in the space of ultradistributions of Beurling type. Moreover, the useful property of the convolution and ultradiferential operator is proved.