{
  "id": "2310.03604",
  "version": "v1",
  "published": "2023-10-05T15:34:07.000Z",
  "updated": "2023-10-05T15:34:07.000Z",
  "title": "Embedding model and de Branges-Rovnyak spaces in Dirichlet spaces",
  "authors": [
    "Carlo Bellavita",
    "Eugenio Alberto Dellepiane"
  ],
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "In this paper we study embeddings between de Branges-Rovnyak spaces $H(b)$ and harmonically weighted Dirichlet spaces $\\mathcal{D}(\\mu)$ in terms of the boundary spectrum of $b$ and the support of the measure $\\mu$, by using elementary reproducing kernel estimates. We completely characterize the embedding between the model spaces $K_u$ and the local Dirichlet spaces $\\mathcal{D}_\\zeta$, and we discuss some applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-05T15:34:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30H45",
      "30H99",
      "46E22",
      "47B32"
    ],
    "keywords": [
      "branges-rovnyak spaces",
      "embedding model",
      "local dirichlet spaces",
      "elementary reproducing kernel estimates",
      "study embeddings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}