{
  "id": "math/0410549",
  "version": "v1",
  "published": "2004-10-26T10:14:20.000Z",
  "updated": "2004-10-26T10:14:20.000Z",
  "title": "Banach frames for alpha-modulation spaces",
  "authors": [
    "Massimo Fornasier"
  ],
  "comment": "24 pages, 1 figure",
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper is concerned with the characterization of $\\alpha$-modulation spaces by Banach frames, i.e., stable and redundant non-orthogonal expansions, constituted of functions obtained by a suitable combination of translation, modulation and dilation of a mother atom. In particular, the parameter $\\alpha \\in [0,1]$ governs the dependence of the dilation factor on the frequency. The result is achieved by exploiting intrinsic properties of localization of such frames. The well-known Gabor and wavelet frames arise as special cases ($\\alpha = 0$) and limiting case ($ \\alpha \\to 1)$, to characterize respectively modulation and Besov spaces. This intermediate theory contributes to a further answer to the theoretical need of a common interpretation and framework between Gabor and wavelet theory and to the construction of new tools for applications in time-frequency analysis, signal processing, and numerical analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-26T10:14:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "42C15",
      "46B25",
      "65T60"
    ],
    "keywords": [
      "banach frames",
      "alpha-modulation spaces",
      "redundant non-orthogonal expansions",
      "wavelet frames arise",
      "intermediate theory contributes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10549F"
    }
  }
}