On the space of ultradistributions vanishing at infinity

Abstract

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

18 pages