{
  "id": "0705.4304",
  "version": "v1",
  "published": "2007-05-29T21:59:21.000Z",
  "updated": "2007-05-29T21:59:21.000Z",
  "title": "Slanted matrices, Banach frames, and sampling",
  "authors": [
    "A. Aldroubi",
    "A. Baskakov",
    "I. Krishtal"
  ],
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "In this paper we present a rare combination of abstract results on the spectral properties of slanted matrices and some of their very specific applications to frame theory and sampling problems. We show that for a large class of slanted matrices boundedness below of the corresponding operator in $\\ell^p$ for some $p$ implies boundedness below in $\\ell^p$ for all $p$. We use the established resultto enrich our understanding of Banach frames and obtain new results for irregular sampling problems. We also present a version of a non-commutative Wiener's lemma for slanted matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-29T21:59:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B37",
      "42C15",
      "47N99",
      "94A20"
    ],
    "keywords": [
      "banach frames",
      "rare combination",
      "irregular sampling problems",
      "abstract results",
      "established resultto enrich"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.4304A"
    }
  }
}