{
  "id": "1811.00990",
  "version": "v1",
  "published": "2018-11-02T17:12:54.000Z",
  "updated": "2018-11-02T17:12:54.000Z",
  "title": "A Centroid for Sections of a Cube in a Function Space, with application to Colorimetry",
  "authors": [
    "Glenn Davis"
  ],
  "comment": "40 pages, 10 figures",
  "categories": [
    "math.FA"
  ],
  "abstract": "The definition of the centroid in finite dimensions does not apply in a function space because of the lack of a translation invariant measure. Another approach, suggested by Nik Weaver, is to use a suitable collection of finite-dimensional subspaces. For a specific collection of subspaces of $L^1[0,1]$, this approach is shown to be successful when the subset is the intersection of a cube with a closed affine subspace of finite codimension. The techniques used are the classical Laplace Transform and saddlepoint method for asymptotics. Applications to spectral reflectance estimation in colorimetry are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-02T17:12:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "45Q05",
      "65R32",
      "41A60",
      "44A10"
    ],
    "keywords": [
      "function space",
      "colorimetry",
      "application",
      "translation invariant measure",
      "spectral reflectance estimation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}