A sequential approach to the convolution of Roumieu ultradistributions

摘要

We consider several general sequential conditions for convolvability of two Roumieu ultradistributions on R-d in the space D'({Mp}) 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 U-{Mp} and U-{Mp} of approximate units and corresponding sequential conditions of integrability of Roumieu ultradistributions, are analogous to the known convolvability conditions in the space D' of distributions and in the space D'({Mp}) of ultradistributions of Beurling type. Moreover, the following property of the convolution and ultradifferential operator P(D) of class {M-p} is proved: if S, T is an element of D'({Mp})(R-d) are convolvable, then