{
  "abstract": "The difference operator $J$ arising from the higher order occurrence for the $L$-orthogonal polynomials is studied using various families of matrix orthogonal polynomials. The matrix orthogonal polynomials determine the polar decomposition of $J$ and its adjoint $J^\\ast$ considered as operators on $\\ell^2(\\mathbb{N})$. The special case of symmetric $J$ leads to the case where the matrix polynomials reduce to diagonal matrix polynomials. The example of the symmetric case with constant coefficients for $L=2$ is discussed in detail.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38603",
  "author_total": 3,
  "authors": [
    {
      "name": "Erik Koelink"
    },
    {
      "name": "Ana Loureiro"
    },
    {
      "name": "Pablo Román"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/af1mpsb0aekyy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38603",
  "fulltext_url": null,
  "id": "af1mpsb0aekyy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38603",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.SP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38603",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/af1mpsb0aekyy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38603",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38603"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Matrix orthogonal polynomials related to diffference operators for $L$-orthogonal polynomials",
  "title_text": "Matrix orthogonal polynomials related to diffference operators for L-orthogonal polynomials",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/af1mpsb0aekyy",
  "venue": "arXiv",
  "versions": []
}