{
  "id": "1910.09257",
  "version": "v1",
  "published": "2019-10-21T10:28:23.000Z",
  "updated": "2019-10-21T10:28:23.000Z",
  "title": "Finding duality for Riesz bases of exponentials on multi-tiles",
  "authors": [
    "Christina Frederick",
    "Kasso Okoudjou"
  ],
  "categories": [
    "math.CA",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "It is known that if $\\Omega \\subset \\mathbb{R}^{d}$ is bounded, measurable set that forms a $k-$tiling of $\\mathbb{R}^d$ when translated by a lattice $L$, there exists a Riesz basis of exponentials for $L^{2}(\\Omega)$ constructed using $k$ translates of the dual lattice $L^*$. In this paper we give an explicit construction of the corresponding bi-orthogonal dual Riesz basis. In addition, we extend the iterative sampling algorithm introduced in prior work to this multivariate setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-21T10:28:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B99",
      "94A20",
      "06D50",
      "42A15"
    ],
    "keywords": [
      "finding duality",
      "exponentials",
      "corresponding bi-orthogonal dual riesz basis",
      "multi-tiles",
      "explicit construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}