# Solution to the Stieltjes moment problem in Gelfand-Shilov spaces

## TL;DR

This paper characterizes the conditions under which the Stieltjes moment problem is solvable in Gelfand-Shilov spaces, providing new insights into ultraholomorphic function spaces and their moment mappings.

## Contribution

It offers a complete characterization of the surjectivity and right inverse existence of the Stieltjes moment mapping in Gelfand-Shilov spaces based on their weight sequences.

## Key findings

- Characterization of surjectivity conditions for the moment mapping.
- Existence criteria for continuous linear right inverses.
- New results on the Borel-Ritt problem in ultraholomorphic spaces.

## Abstract

We characterize the surjectivity and the existence of a continuous linear right inverse of the Stieltjes moment mapping on Gelfand-Shilov spaces, both of Beurling and Roumieu type, in terms of their defining weight sequence. As a corollary, we obtain some new results about the Borel-Ritt problem in spaces of ultraholomorphic functions on the upper half-plane.