{
  "id": "1108.5628",
  "version": "v1",
  "published": "2011-08-29T16:16:55.000Z",
  "updated": "2011-08-29T16:16:55.000Z",
  "title": "Reconstruction of Paley-Wiener functions on the Heisenberg group",
  "authors": [
    "Isaac Pesenson"
  ],
  "journal": "Voronezh Winter Mathematical Schools, 207-216, Amer. Math. Soc. Transl. Ser. 2, 184, Amer. Math. Soc., Providence, RI, 1998",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $M$ be a Riemmanian manifold with bounded geometry. We consider a generalization of Paley-Wiener functions and Lagrangian splines on $M$. An analog of the Paley-Wiener theorem is given. We also show that every Paley-Wiener function on a manifold is uniquely determined by its values on some discrete sets of points. The main result of the paper is a generalization of the Whittaker-Shannon formula for reconstruction of a Paley-Wiener function from its values on a discrete set. It is shown that every Paley- Wiener function on $M$ is a limit of some linear combinations of fundamental solutions of the powers of the Laplace-Beltrami operator. The result is new even in the one-dimentional case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-29T16:16:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "paley-wiener function",
      "heisenberg group",
      "reconstruction",
      "discrete set",
      "laplace-beltrami operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.5628P"
    }
  }
}