{
  "id": "1105.1373",
  "version": "v1",
  "published": "2011-05-06T18:48:36.000Z",
  "updated": "2011-05-06T18:48:36.000Z",
  "title": "Moments and the Range of the Derivative",
  "authors": [
    "Eugen J. Ionascu",
    "Richard Stephens"
  ],
  "comment": "13 pages, 1 figure",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this note we introduce three problems related to the topic of finite Hausdorff moments. Generally speaking, given the first n+1 (n in N or n=0) moments, alpha(0), alpha(1),..., alpha(n), of a real-valued continuously differentiable function f defined on [0,1], what can be said about the size of the image of df/dx? We make the questions more precise and we give answers in the cases of three or fewer moments and in some cases for four moments. In the general situation of n+1 moments, we show that the range of the derivative should contain the convex hull of a set of n numbers calculated in terms of the Bernstein polynomials, x^k(1-x)^{n+1-k}, k=1,2,...,n, which turn out to involve expressions just in terms of the given moments alpha(i), i=0,1,2,...n. In the end we make some conjectures about what may be true in terms of the sharpness of the interval range mentioned before.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-06T18:48:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A24"
    ],
    "keywords": [
      "derivative",
      "finite hausdorff moments",
      "fewer moments",
      "interval range",
      "convex hull"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.1373I"
    }
  }
}