{
  "id": "1804.03577",
  "version": "v2",
  "published": "2018-04-10T14:57:37.000Z",
  "updated": "2019-01-09T16:25:51.000Z",
  "title": "Parseval frames of piecewise constant functions",
  "authors": [
    "Dorin Ervin Dutkay",
    "Rajitha Ranasinghe"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We present a way to construct Parseval frames of piecewise constant functions for $L^2[0,1]$. The construction is similar to the generalized Walsh bases. It is based on iteration of operators that satisfy a Cuntz-type relation, but without the isometry property. We also show how the Parseval frame can be dilated to an orthonormal basis and the operators can be dilated to true Cuntz isometries.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2019-01-09T16:25:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "piecewise constant functions",
      "construct parseval frames",
      "true cuntz isometries",
      "orthonormal basis",
      "generalized walsh bases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}