{
  "id": "0809.4647",
  "version": "v1",
  "published": "2008-09-26T14:35:54.000Z",
  "updated": "2008-09-26T14:35:54.000Z",
  "title": "Series expansions in Fréchet spaces and their duals; construction of Fréchet frames",
  "authors": [
    "Stevan Pilipović",
    "Diana T. Stoeva"
  ],
  "journal": "Journal of Approximation Theory 163 (2011), 1729-1747",
  "categories": [
    "math.FA"
  ],
  "abstract": "Frames for Fr\\'echet spaces $X_F$ with respect to Fr\\'echet sequence spaces $\\Theta_F$ are studied and conditions, implying series expansions in $X_F$ and $X_F^*$, are determined. If $\\{g_i\\}$ is a $\\Theta_0$-frame for $X_0$, we construct a sequence $\\{X_s\\}_{s\\in {\\mathbb N}_0}$, $X_s\\subset X_{s-1}$, $s\\in {\\mathbb N}$, for given $\\Theta_F$, respectively a sequence $\\{\\Theta_s\\}_{s\\in {\\mathbb N}_0}$, $\\Theta_s\\subset \\Theta_{s-1}$, $s\\in {\\mathbb N}$, for given $X_F$, so that $\\{g_i\\}$ is a pre-$F$-frame (or $F$-frame) for $X_F$ with respect to $\\Theta_F$ under different assumptions given on $X_0$, $\\Theta_0$, $\\Theta_F$ or $X_0$, $\\Theta_0$, $X_F$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-26T14:35:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15",
      "42C20",
      "46A13",
      "46A45"
    ],
    "keywords": [
      "fréchet spaces",
      "fréchet frames",
      "construction",
      "frechet sequence spaces",
      "frechet spaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4647P"
    }
  }
}