{
  "id": "2104.01216",
  "version": "v1",
  "published": "2021-04-02T19:30:38.000Z",
  "updated": "2021-04-02T19:30:38.000Z",
  "title": "Generalised Sylvester-Kac matrices generated by linear differential equations with polynomial solutions",
  "authors": [
    "Alexander Dyachenko",
    "Mikhail Tyaglov"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "A method of generating differential operators is used to solve the spectral problem for a generalisation of the Sylvester-Kac matrix. As a by-product, we find a linear differential operator with polynomial coefficients of the first order that has a finite sequence of polynomial eigenfunctions generalising the operator considered by M. Kac.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-02T19:30:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A18",
      "47B36",
      "34A05",
      "34L10",
      "34L05"
    ],
    "keywords": [
      "linear differential equations",
      "generalised sylvester-kac matrices",
      "sylvester-kac matrix",
      "polynomial solutions",
      "linear differential operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}