A sequential approach to the convolution of Roumieu ultradistributions (Q2656195)

The author studies the convolvability of non-quasi-analytic Roumieu ultradistributions. The main result states that the existence of convolution of two Roumieu ultradistributions can be characterised in a sequential manner by employing so-called approximate units; an approximate unit is a sequence of ultradifferentiable functions with compact support which tends to \(1\) and is bounded in the ultradifferentiable analog of \(\mathcal{D}_{L^{\infty}}\).