{
  "id": "2006.03734",
  "version": "v1",
  "published": "2020-06-05T23:12:00.000Z",
  "updated": "2020-06-05T23:12:00.000Z",
  "title": "On near orthogonality of the Banach frames of the wave packet spaces",
  "authors": [
    "Dimitri Bytchenkoff"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In solving scientific, engineering or pure mathematical problems one is often faced with a need to approximate the function of a given class by the linear combination of a preferably small number of functions that are localised one way or another both in the time and frequency domain. Over the last seventy years or so a range of systems of thus localised functions have been developed to allow the decomposition and synthesis of functions of various classes. The most prominent examples of such systems are Gabor functions, wavelets, ridgelets, curvelets, shearlets and wave atoms. We recently introduced a family of quasi-Banach spaces -- which we called wave packet spaces -- that encompasses all those classes of functions whose elements have sparse expansions in one of the above-mentioned systems, supplied them with Banach frames and provided their atomic decompositions. Herein we prove that the Banach frames and sets of atoms of the wave packet spaces are well localised or, more specifically, that they are near orthogonal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-05T23:12:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "42C15",
      "42C40"
    ],
    "keywords": [
      "wave packet spaces",
      "banach frames",
      "orthogonality",
      "pure mathematical problems",
      "wave atoms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}