{
  "id": "0711.2381",
  "version": "v1",
  "published": "2007-11-15T11:34:47.000Z",
  "updated": "2007-11-15T11:34:47.000Z",
  "title": "Sufficient conditions for the convergence of the Magnus expansion",
  "authors": [
    "Fernando Casas"
  ],
  "comment": "20 pages",
  "journal": "J. Phys. A: Math. Theor. 40 (2007), 15001-15017",
  "doi": "10.1088/1751-8113/40/50/006",
  "categories": [
    "math.CA"
  ],
  "abstract": "Two different sufficient conditions are given for the convergence of the Magnus expansion arising in the study of the linear differential equation $Y' = A(t) Y$. The first one provides a bound on the convergence domain based on the norm of the operator $A(t)$. The second condition links the convergence of the expansion with the structure of the spectrum of $Y(t)$, thus yielding a more precise characterization. Several examples are proposed to illustrate the main issues involved and the information on the convergence domain provided by both conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-15T11:34:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A12",
      "34A30"
    ],
    "keywords": [
      "sufficient conditions",
      "convergence domain",
      "linear differential equation",
      "second condition links",
      "precise characterization"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2007,
      "month": "Dec",
      "volume": 40,
      "number": 50,
      "pages": 15001
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007JPhA...4015001C"
    }
  }
}