{
  "id": "1704.05699",
  "version": "v1",
  "published": "2017-04-19T11:34:54.000Z",
  "updated": "2017-04-19T11:34:54.000Z",
  "title": "Fourier series of the curl operator and Sobolev spaces",
  "authors": [
    "R. S. Saks"
  ],
  "comment": "in Russian",
  "categories": [
    "math.FA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The properties of curl and gradient of divergence operators in the domain $G$ of three-dimensional space are described. The self-conjugacy of these operators in the subspaces $\\mathbf{L}_{2}(G) $ and the basis property of the system of eigenfunctions are discussed. Exact formulas are founded for solving boundary value problems in a ball and the conditions for the decomposition of vector functions into Fourier series in eigenfunctions of the curl and the gradient of divergence operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-19T11:34:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fourier series",
      "curl operator",
      "sobolev spaces",
      "divergence operators",
      "solving boundary value problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "ru",
      "license": "arXiv",
      "status": "editable"
    }
  }
}