{
  "id": "2304.07185",
  "version": "v1",
  "published": "2023-04-14T14:55:36.000Z",
  "updated": "2023-04-14T14:55:36.000Z",
  "title": "Bounded Poincaré operators for twisted and BGG complexes",
  "authors": [
    "Andreas Čap",
    "Kaibo Hu"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "math.AP",
    "math.FA"
  ],
  "abstract": "We construct bounded Poincar\\'e operators for twisted complexes and BGG complexes with a wide class of function classes (e.g., Sobolev spaces) on bounded Lipschitz domains. These operators are derived from the de Rham versions using BGG diagrams and, for vanishing cohomology, satisfy the homotopy identity $dP+Pd=I$ in degrees $>0$. The operators preserve polynomial classes if the de Rham versions do so.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-14T14:55:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bgg complexes",
      "operators preserve polynomial classes",
      "rham versions",
      "construct bounded poincare operators",
      "wide class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}