{
  "id": "0809.4053",
  "version": "v1",
  "published": "2008-09-23T23:36:11.000Z",
  "updated": "2008-09-23T23:36:11.000Z",
  "title": "Some extremal functions in Fourier analysis, III",
  "authors": [
    "Emanuel Carneiro",
    "Jeffrey D. Vaaler"
  ],
  "comment": "26 pages. Submitted",
  "journal": "Constructive Approximation, v. 31, p. 259-288, 2010",
  "doi": "10.1007/s00365-009-9050-6",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "We obtain the best approximation in $L^1(\\R)$, by entire functions of exponential type, for a class of even functions that includes $e^{-\\lambda|x|}$, where $\\lambda >0$, $\\log |x|$ and $|x|^{\\alpha}$, where $-1 < \\alpha < 1$. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-23T23:36:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A30",
      "41A52",
      "42A05"
    ],
    "keywords": [
      "fourier analysis",
      "extremal functions",
      "trigonometric polynomials",
      "best approximation",
      "periodic versions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4053C"
    }
  }
}