{
  "id": "1609.04438",
  "version": "v1",
  "published": "2016-09-14T20:37:08.000Z",
  "updated": "2016-09-14T20:37:08.000Z",
  "title": "Local approximation of arbitrary functions by solutions of nonlocal equations",
  "authors": [
    "Serena Dipierro",
    "Ovidiu Savin",
    "Enrico Valdinoci"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that any function can be locally approximated by solutions of prescribed linear equations of nonlocal type. In particular, we show that every function is locally $s$-caloric, up to a small error. The case of non-elliptic and non-parabolic operators is taken into account as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-14T20:37:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arbitrary functions",
      "nonlocal equations",
      "local approximation",
      "non-parabolic operators",
      "prescribed linear equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}