{
  "id": "math/0606016",
  "version": "v2",
  "published": "2006-06-01T06:51:50.000Z",
  "updated": "2006-12-18T09:02:25.000Z",
  "title": "Norms of Toeplitz Matrices with Fisher-Hartwig Symbols",
  "authors": [
    "Albrecht Boettcher",
    "Jani Virtanen"
  ],
  "comment": "16 pages",
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "We describe the asymptotics of the spectral norm of finite Toeplitz matrices generated by functions with Fisher-Hartwig singularities as the matrix dimension goes to infinity. In the case of positive generating functions, our result provides the asymptotics of the largest eigenvalue, which is of interest in time series with long-range memory.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-12-18T09:02:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B35",
      "15A60",
      "62M10",
      "65F35"
    ],
    "keywords": [
      "fisher-hartwig symbols",
      "spectral norm",
      "finite toeplitz matrices",
      "fisher-hartwig singularities",
      "asymptotics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6016B"
    }
  }
}