{
  "id": "1006.4323",
  "version": "v2",
  "published": "2010-06-22T16:30:18.000Z",
  "updated": "2010-09-09T15:23:50.000Z",
  "title": "The size of exponential sums on intervals of the real line",
  "authors": [
    "Tamás Erdélyi",
    "Kaveh Khodjasteh",
    "Lorenza Viola"
  ],
  "comment": "Fixed minor problems and added a new remark",
  "categories": [
    "math.CA",
    "quant-ph"
  ],
  "abstract": "We prove that there is a constant $c > 0$ depending only on $M \\geq 1$ and $\\mu \\geq 0$ such that $$\\int_y^{y+a}{|g(t)| \\, dt} \\geq \\exp (-c/(a\\delta))\\,, a \\in (0,\\pi]\\,,$$ for every $g$ of the form $$g(t) = \\sum_{j=0}^n{a_j e^{i\\lambda_jt}}, a_j \\in {\\Bbb C}, \\enskip |a_j| \\leq Mj^\\mu\\,, \\enskip |a_0|=1\\,, \\enskip n \\in {\\Bbb N} \\,,$$ where the exponents $\\lambda_j \\in {\\Bbb C}$ satisfy $$\\text{\\rm Re}(\\lambda_0) = 0\\,, \\qquad \\text{\\rm Re}(\\lambda_j) \\geq j\\delta > 0\\,, j=1,2,\\ldots\\,,$$ and for every subinterval $[y,y+a]$ of the real line. Establishing inequalities of this variety is motivated by problems in physics.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-09-09T15:23:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30E10",
      "26D05",
      "42A05"
    ],
    "keywords": [
      "real line",
      "exponential sums",
      "subinterval",
      "establishing inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.4323E"
    }
  }
}