{
  "id": "1411.5610",
  "version": "v1",
  "published": "2014-11-20T17:20:46.000Z",
  "updated": "2014-11-20T17:20:46.000Z",
  "title": "Nonuniform Sampling and Recovery of Bandlimited Functions in Higher Dimensions",
  "authors": [
    "Keaton Hamm"
  ],
  "comment": "14 pages. Submitted",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "We provide sufficient conditions on a family of functions $(\\phi_\\alpha)_{\\alpha\\in A}:\\mathbb{R}^d\\to\\mathbb{R}^d$ for sampling of multivariate bandlimited functions at certain nonuniform sequences of points in $\\mathbb{R}^d$. We consider interpolation of functions whose Fourier transform is supported in some small ball in $\\mathbb{R}^d$ at scattered points $(x_j)_{j\\in\\mathbb{N}}$ such that the complex exponentials $\\left(e^{-i\\langle x_j,\\cdot\\rangle}\\right)_{j\\in\\mathbb{N}}$ form a Riesz basis for the $L_2$ space of a convex body containing the ball. Recovery results as well as corresponding approximation orders in terms of the parameter $\\alpha$ are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-20T17:20:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A05",
      "41A30",
      "42C30"
    ],
    "keywords": [
      "higher dimensions",
      "nonuniform sampling",
      "sufficient conditions",
      "corresponding approximation orders",
      "recovery results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.5610H"
    }
  }
}