On the space of ultradistributions vanishing at infinity

Abstract

We study the structural and linear topological properties of the space \(\dot{\mathcal {B}}^{\prime *}_{\omega }\) of ultradistributions vanishing at infinity (with respect to a weight function \(\omega \)). Particularly, we show the first structure theorem for \(\dot{\mathcal {B}}^{\prime *}_{\omega }\) under weaker hypotheses than were known so far. As an application, we determine the structure of the S-asymptotic behavior of ultradistributions.