Some results on ultradifferential convolution property of ultradistributions

Abstract

We consider some sequential conditions for the convolvability of two ultradistributions, specifically the Roumieu ultradistributions defined on the space of all ultradifferentiable functions  Dn{M_p}  in the space Dn'{M_p}  and show the similarities between these conditions in the sense of Mincheva-Kaminska S. The sequential conditions are based on the use of approximate identities which satisfy certain conditions to be a Banach algebra for the space Dn{M_p} . We present an equivalent result involving the convolution of the differentiability of two Roumieu ultradistributions with equivalent norm condition.