# On the space of ultradistributions vanishing at infinity

## TL;DR

This paper investigates the topological structure of ultradistributions that vanish at infinity, providing a new structure theorem under weaker conditions and analyzing their asymptotic behavior.

## Contribution

It presents the first structure theorem for the space of ultradistributions vanishing at infinity under less restrictive hypotheses.

## Key findings

- Established a new structure theorem for ultradistributions vanishing at infinity.
- Determined the S-asymptotic behavior of ultradistributions.
- Extended understanding of the topological properties of ultradistribution spaces.

## Abstract

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