{
  "id": "2301.12949",
  "version": "v1",
  "published": "2023-01-30T14:45:31.000Z",
  "updated": "2023-01-30T14:45:31.000Z",
  "title": "Moment problem for algebras generated by a nuclear space",
  "authors": [
    "Maria Infusino",
    "Salma Kuhlmann",
    "Tobias Kuna",
    "Patrick Michalski"
  ],
  "comment": "30 pages",
  "categories": [
    "math.FA",
    "math.PR"
  ],
  "abstract": "We establish a criterion for the existence of a representing Radon measure for linear functionals defined on a unital commutative real algebra $A$, which we assume to be generated by a vector space $V$ endowed with a Hilbertian seminorm $q$. Such a general criterion provides representing measures with support contained in the space of characters of $A$ whose restrictions to $V$ are $q-$continuous. This allows us in turn to prove existence results for the case when $V$ is endowed with a nuclear topology. In particular, we apply our findings to the symmetric tensor algebra of a nuclear space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-30T14:45:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "44A60",
      "46M40",
      "28C20"
    ],
    "keywords": [
      "nuclear space",
      "moment problem",
      "symmetric tensor algebra",
      "unital commutative real algebra",
      "representing radon measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}