{
  "id": "1801.08378",
  "version": "v1",
  "published": "2018-01-25T12:34:27.000Z",
  "updated": "2018-01-25T12:34:27.000Z",
  "title": "On the local integrability condition for generalised translation-invariant systems",
  "authors": [
    "Jordy Timo van Velthoven"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper considers the local integrability condition for generalised translation-invariant systems and its relation to the Calder\\'on integrability condition, the temperateness condition and the uniform counting estimate. It is shown that sufficient and necessary conditions on a generalised translation-invariant system to satisfy the local integrability condition are closely related to lower and upper bounds on the number of lattice points that intersect with the translates of a compact set. The results are complemented by examples that illustrate the crucial interplay between the translation subgroups and the generating functions of the system for satisfying the local integrability condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-25T12:34:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C40",
      "43A32",
      "42C15",
      "43A70"
    ],
    "keywords": [
      "local integrability condition",
      "generalised translation-invariant system",
      "calderon integrability condition",
      "lattice points",
      "temperateness condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}