{
  "id": "2403.14388",
  "version": "v1",
  "published": "2024-03-21T13:28:27.000Z",
  "updated": "2024-03-21T13:28:27.000Z",
  "title": "Quarklet Characterizations for bivariate Bessel-Potential Spaces on the Unit Square via Tensor Products",
  "authors": [
    "Marc Hovemann"
  ],
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "In this paper we deduce new characterizations for bivariate Bessel-Potential spaces defined on the unit square via B-spline quarklets. For that purpose in a first step we use univariate boundary adapted quarklets to describe univariate Bessel-Potential spaces on intervals. To obtain the bivariate characterizations a recent result of Hansen and Sickel is applied. It yields that each bivariate Bessel-Potential space on a square can be written as an intersection of function spaces which have a tensor product structure. Hence our main result is a characterization of bivariate Bessel-Potential spaces on squares in terms of quarklets that are tensor products of univariate quarklets on intervals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-21T13:28:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35"
    ],
    "keywords": [
      "bivariate bessel-potential space",
      "unit square",
      "quarklet characterizations",
      "tensor product structure",
      "univariate bessel-potential spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}