{
  "id": "1212.0148",
  "version": "v3",
  "published": "2012-12-01T18:45:55.000Z",
  "updated": "2013-09-24T05:28:18.000Z",
  "title": "Energy Measures of Harmonic Functions on the Sierpiński Gasket",
  "authors": [
    "Renee Bell",
    "Ching-Wei Ho",
    "Robert S. Strichartz"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study energy measures on SG based on harmonic functions. We characterize the positive energy measures through studying the bounds of Radon-Nikodym derivatives with respect to the Kusuoka measure. We prove a limited continuity of the derivative on the graph $V_*$ and express the average value of the derivative on a whole cell as a weighted average of the values on the boundary vertices. We also prove some characterizations and properties of the weights.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-09-24T05:28:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80"
    ],
    "keywords": [
      "harmonic functions",
      "sierpiński gasket",
      "study energy measures",
      "positive energy measures",
      "radon-nikodym derivatives"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.0148B"
    }
  }
}