{
  "id": "1208.3799",
  "version": "v1",
  "published": "2012-08-19T01:45:15.000Z",
  "updated": "2012-08-19T01:45:15.000Z",
  "title": "A New Proof Of The Asymptotic Limit Of The $Lp$ Norm Of The Sinc Function",
  "authors": [
    "R. Kerman",
    "S. Spektor"
  ],
  "comment": "3 pages",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "We improve on the inequality $\\displaystyle{\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt\\leq \\frac{1}{\\sqrt p}, {0.2 cm}p\\geq 1,}$ showing that $\\displaystyle{\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt\\leq C(p) \\frac{\\sqrt{3/\\pi}}{\\sqrt p},}$ with $\\displaystyle{\\lim_{p\\longrightarrow \\infty} C(p)=1,}$ and indeed that {align*} \\displaystyle{\\lim_{p\\longrightarrow \\infty}\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt/ \\frac{\\sqrt{3/\\pi}}{\\sqrt p}=1.} {align*}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-19T01:45:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic limit",
      "sinc function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.3799K"
    }
  }
}