{
  "id": "2307.08081",
  "version": "v1",
  "published": "2023-07-16T15:37:07.000Z",
  "updated": "2023-07-16T15:37:07.000Z",
  "title": "Banded matrices and their orthogonality",
  "authors": [
    "Amílcar Branquinho",
    "Ana Foulquié-Moreno",
    "Manuel Mañas"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2203.13578",
  "categories": [
    "math.CA"
  ],
  "abstract": "Banded bounded matrices, which represent non normal operators, of oscillatory type that admit a positive bidiagonal factorization are considered. To motivate the relevance of the oscillatory character the Favard theorem for Jacobi matrices is revisited and it is shown that after an adequate shift of the Jacobi matrix one gets an oscillatory matrix. In this work we present a spectral theorem for this type of operators and show how the theory of multiple orthogonal polynomials apply.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-16T15:37:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "33C45",
      "33C47",
      "60J10",
      "60Gxx"
    ],
    "keywords": [
      "banded matrices",
      "orthogonality",
      "represent non normal operators",
      "jacobi matrix",
      "multiple orthogonal polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}