The Stieltjes moment problem in Gelfand-Shilov spaces defined by weight sequences in the absence of derivation closedness

Fuente: arXiv
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Hauptverfasser: Jiménez-Garrido, Javier, Miguel-Cantero, Ignacio, Sanz, Javier, Schindl, Gerhard
Format: Preprint
Veröffentlicht: 2025
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author Jiménez-Garrido, Javier
Miguel-Cantero, Ignacio
Sanz, Javier
Schindl, Gerhard
author_facet Jiménez-Garrido, Javier
Miguel-Cantero, Ignacio
Sanz, Javier
Schindl, Gerhard
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_06878
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Stieltjes moment problem in Gelfand-Shilov spaces defined by weight sequences in the absence of derivation closedness
Jiménez-Garrido, Javier
Miguel-Cantero, Ignacio
Sanz, Javier
Schindl, Gerhard
Functional Analysis
Classical Analysis and ODEs
30E05, 44A60, 46F05
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.
title The Stieltjes moment problem in Gelfand-Shilov spaces defined by weight sequences in the absence of derivation closedness
topic Functional Analysis
Classical Analysis and ODEs
30E05, 44A60, 46F05
url https://arxiv.org/abs/2511.06878