# Asymptotic boundedness and moment asymptotic expansion in ultradistribution spaces

## TL;DR

This paper develops structural theorems for ultradistributions related to asymptotic boundedness and moment asymptotic expansion, providing characterizations and introducing a uniform variant in one-dimensional spaces.

## Contribution

It introduces new structural theorems for S-asymptotic and quasiasymptotic boundedness of ultradistributions and characterizes those satisfying the moment asymptotic expansion in one dimension.

## Key findings

- Full characterization of ultradistributions with moment asymptotic expansion
- Introduction of a uniform variant of the moment asymptotic expansion
- Structural theorems for S-asymptotic and quasiasymptotic boundedness

## Abstract

We obtain structural theorems for the so-called S-asymptotic and quasiasymptotic boundedness of ultradistributions. Using these results, we then analyze the moment asymptotic expansion (MAE), providing a full characterization of those ultradistributions satisfying this asymptotic formula in the one-dimensional case. We also introduce and study a uniform variant of the MAE.