{
  "id": "1311.3399",
  "version": "v1",
  "published": "2013-11-14T07:42:09.000Z",
  "updated": "2013-11-14T07:42:09.000Z",
  "title": "Jackson's inequality in the complex plane and the Lojasiewicz-Siciak inequality of Green's function",
  "authors": [
    "Leokadia Bialas-Ciez",
    "Raimondo Eggink"
  ],
  "categories": [
    "math.CV"
  ],
  "abstract": "We prove a generalization of Dunham Jackson's famous approximation inequality to the case of compact sets in the complex plane admitting both upper and lower bounds for their Green's functions, i.e. the well known Holder Continuity Property (HCP) and the less known but crucial Lojasiewicz-Siciak inequality (LS). Moreover, we show that (LS) is a necessary condition for our Jackson type inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-14T07:42:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex plane",
      "greens function",
      "jacksons inequality",
      "dunham jacksons famous approximation inequality",
      "jackson type inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.3399B"
    }
  }
}