{
  "id": "1801.06804",
  "version": "v1",
  "published": "2018-01-21T10:36:17.000Z",
  "updated": "2018-01-21T10:36:17.000Z",
  "title": "On Taylor coefficients of smooth functions",
  "authors": [
    "Avner Kiro"
  ],
  "comment": "6 figures",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "We study the Borel map, which maps infinitely differentiable functions on an interval to the jets of their Taylor coefficients at a given point in the interval. Our main results include a complete description of the image of the Borel map for Beurling classes of smooth functions and a moment-type summation method which allows one to recover a function from its Taylor jet. A surprising feature of this description is an unexpected threshold at the logarithmic class. Another interesting finding is a \"duality\" between non-quasianalytic and quasianalytic classes, which reduces the description of the image of the Borel map for non-quasianalytic classes to the one for the corresponding quasianalytic classes, and complements classical results of Carleson and Ehrenpreis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-21T10:36:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smooth functions",
      "taylor coefficients",
      "borel map",
      "quasianalytic classes",
      "moment-type summation method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}