# Injectivity and surjectivity of the Stieltjes moment mapping in Gelfand-Shilov spaces

## TL;DR

This paper investigates the conditions under which the Stieltjes moment mapping is injective or surjective within Gelfand-Shilov spaces, linking these properties to growth conditions of defining weight sequences.

## Contribution

It provides a characterization of injectivity and surjectivity of the Stieltjes moment mapping in Gelfand-Shilov spaces based on weight sequence growth conditions.

## Key findings

- Characterization of injectivity conditions
- Characterization of surjectivity conditions
- Analysis of a related moment problem at the origin

## Abstract

The Stieltjes moment problem is studied in the framework of general Gelfand-Shilov spaces defined via weight sequences. We characterize the injectivity and surjectivity of the Stieltjes moment mapping, sending a function to its sequence of moments, in terms of growth conditions for the defining weight sequence. Finally, a related moment problem at the origin is studied.