{
  "id": "1508.07150",
  "version": "v1",
  "published": "2015-08-28T09:44:52.000Z",
  "updated": "2015-08-28T09:44:52.000Z",
  "title": "Schrödinger Operators With $A_\\infty$ Potentials",
  "authors": [
    "Andrew Raich",
    "Michael Tinker"
  ],
  "comment": "15 pages. Comments welcome!",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the heat kernel $p(x,y,t)$ associated to the real Schr\\\"odinger operator $H = -\\Delta + V$ on $L^2(\\mathbb{R}^n)$, $n \\geq 1$. Our main result is a pointwise upper bound on $p$ when the potential $V \\in A_\\infty$. In the case that $V\\in RH_\\infty$, we also prove a lower bound. Additionally, we compute $p$ explicitly when $V$ is a quadratic polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-28T09:44:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K08",
      "35J10",
      "32W30"
    ],
    "keywords": [
      "schrödinger operators",
      "quadratic polynomial",
      "heat kernel",
      "main result",
      "lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150807150R"
    }
  }
}