{
  "id": "2204.06244",
  "version": "v1",
  "published": "2022-04-13T08:30:52.000Z",
  "updated": "2022-04-13T08:30:52.000Z",
  "title": "Basisness and completeness of Fucik eigenfunctions for the Neumann Laplacian",
  "authors": [
    "Falko Baustian",
    "Vladimir Bobkov"
  ],
  "comment": "26 pages, 3 figures",
  "categories": [
    "math.CA",
    "math.AP",
    "math.SP"
  ],
  "abstract": "We investigate the basis properties of sequences of Fucik eigenfunctions of the one-dimensional Neumann Laplacian. We show that any such sequence is complete in $L^2(0,\\pi)$ and a Riesz basis in the subspace of functions with zero mean. Moreover, we provide sufficient assumptions on Fucik eigenvalues which guarantee that the corresponding Fucik eigenfunctions form a Riesz basis in $L^2(0,\\pi)$ and we explicitly describe the corresponding biorthogonal system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-13T08:30:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34L10",
      "34B08",
      "47A70"
    ],
    "keywords": [
      "riesz basis",
      "completeness",
      "one-dimensional neumann laplacian",
      "corresponding fucik eigenfunctions form",
      "zero mean"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}