The Stieltjes Moment Problem in Gelfand-Shilov Spaces Defined by Weight Sequences in the Absence of Derivation Closedness
Abstract
The Stieltjes moment problem is studied in a new framework within the general Gelfand-Shilov spaces defined via weight sequences. The novelty consists of allowing for a naturally larger target space for the moment mapping, which sends a function to its sequence of Stieltjes moments. The motivation comes from a recent version of the Borel-Ritt theorem, concerning the surjectivity of the Borel mapping in Carleman-Roumieu ultraholomorphic classes in sectors, whose defining weight sequence is subject to the condition, weaker than derivation closedness, of having shifted moments. The injectivity and surjectivity of the moment mapping in this new setting is studied and, in some cases, characterized. Finally, results are provided for general weight sequences of fast and regular enough growth when the condition of shifted moments fails to hold.
Fields of Study & Subjects
Holomorphic and Operator Theory
Meromorphic and Entire Functions
Analytic and geometric function theory
Publication details
- Journal / source
- Results in Mathematics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 81
- Issue
- 5
- Pages
- 139–139
- Publication date
- 26 June 2026
- Language
- EN