{
  "annotation_id": "9d754eac-83dd-4eb6-a879-a04012205361",
  "date_created": "2026-03-02T18:02:10.465000Z",
  "date_modified": "2026-03-02T18:02:10.465000Z",
  "file_hash": "833b2fc6443c98d880f42d4999da5e80948746b345f01762d2835f24ceb72647",
  "private": false,
  "record": {
    "abstract": "We consider the generalized Segal-Bargmann transform, defined in terms of the\nheat operator, for a noncompact symmetric space of the complex type. For radial\nfunctions, we show that the Segal-Bargmann transform is a unitary map onto a\ncertain L^2 space of meromorphic functions. For general functions, we give an\ninversion formula for the Segal-Bargmann transform, involving integration\nagainst an \"unwrapped\" version of the heat kernel for the dual compact\nsymmetric space. Both results involve delicate cancellations of singularities.",
    "arxiv_id": "quant-ph/0409118",
    "authors": [
      "Brian C. Hall",
      "Jeffrey J. Mitchell"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "journal_ref": "J. Functional Analysis 227 (2005), 338-371",
    "title": "The Segal-Bargmann transform for noncompact symmetric spaces of the   complex type",
    "url": "https://arxiv.org/abs/quant-ph/0409118"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6cc68942-3e3b-4cf2-a21c-5ab491b35bc7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}