{
  "id": "2502.00727",
  "version": "v1",
  "published": "2025-02-02T09:17:30.000Z",
  "updated": "2025-02-02T09:17:30.000Z",
  "title": "Inner and characteristic functions in polydiscs",
  "authors": [
    "Ramlal Debnath",
    "Deepak K. Pradhan",
    "Jaydeb Sarkar"
  ],
  "comment": "43 pages",
  "categories": [
    "math.FA",
    "math.CV",
    "math.OA"
  ],
  "abstract": "Characteristic functions of linear operators are analytic functions that serve as complete unitary invariants. Such functions, as long as they are built in a natural and canonical manner, provide representations of inner functions on a suitable domain and make significant contributions to the development of various theories in Hilbert function spaces. In this paper, we solve this problem in polydiscs. In particular, we present a concrete description of the characteristic functions of tuples of commuting pure contractions and, consequently, provide a description of inner functions on polydiscs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-02T09:17:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46J15",
      "47A15",
      "30H05",
      "47A56",
      "32A35",
      "30J05"
    ],
    "keywords": [
      "characteristic functions",
      "inner functions",
      "hilbert function spaces",
      "complete unitary invariants",
      "analytic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}