{
  "id": "1007.4043",
  "version": "v1",
  "published": "2010-07-23T05:27:43.000Z",
  "updated": "2010-07-23T05:27:43.000Z",
  "title": "A Density Condition for Interpolation on the Heisenberg Group",
  "authors": [
    "Bradley Currey",
    "Azita Mayeli"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $N$ be the Heisenberg group. We consider left-invariant multiplicity free subspaces of $L^2(N)$. We prove a necessary and sufficient density condition in order that such subspaces possess the interpolation property with respect to a class of discrete subsets of $N$ that includes the integer lattice. We exhibit a concrete example of a subspace that has interpolation for the integer lattice, and we also prove a necessary and sufficient condition for shift invariant subspaces to possess a singly-generated orthonormal basis of translates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-23T05:27:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "92A20",
      "43A80"
    ],
    "keywords": [
      "heisenberg group",
      "left-invariant multiplicity free subspaces",
      "integer lattice",
      "sufficient density condition",
      "shift invariant subspaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.4043C"
    }
  }
}