{
  "id": "1803.03066",
  "version": "v1",
  "published": "2018-03-08T12:35:11.000Z",
  "updated": "2018-03-08T12:35:11.000Z",
  "title": "The complex moment problem: determinacy and extendibility",
  "authors": [
    "D. Cichoń",
    "J. Stochel. F. H. Szafraniec"
  ],
  "comment": "21 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Complex moment sequences are exactly those which admit positive definite extensions on the integer lattice points of the upper diagonal half-plane. Here we prove that the aforesaid extension is unique provided the complex moment sequence is determinate and its only representing measure has no atom at $0$. The question of converting the relation is posed as an open problem. A partial solution to this problem is established when at least one of representing measures is supported in a plane algebraic curve whose intersection with every straight line passing through $0$ is at most one point set. Further study concerns representing measures whose supports are Zariski dense in $\\mathbb C$ as well as complex moment sequences which are constant on a family of parallel \"Diophantine lines\". All this is supported by a bunch of illustrative examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-08T12:35:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "44A60",
      "43A35",
      "14P05"
    ],
    "keywords": [
      "complex moment problem",
      "complex moment sequence",
      "extendibility",
      "determinacy",
      "upper diagonal half-plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}