{
  "id": "1106.1970",
  "version": "v3",
  "published": "2011-06-10T07:04:22.000Z",
  "updated": "2011-11-15T01:22:44.000Z",
  "title": "A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups",
  "authors": [
    "Maria Gordina",
    "Tai Melcher"
  ],
  "comment": "Initially posted in June 2011, with minor corrections in November 2011",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $G$ denote an infinite-dimensional Heisenberg-like group, which is a class of infinite-dimensional step 2 stratified Lie groups. We consider holomorphic functions on $G$ that are square integrable with respect to a heat kernel measure which is formally subelliptic, in the sense that all appropriate finite dimensional projections are smooth measures. We prove a unitary equivalence between a subclass of these square integrable holomorphic functions and a certain completion of the universal enveloping algebra of the \"Cameron-Martin\" Lie subalgebra. The isomorphism defining the equivalence is given as a composition of restriction and Taylor maps.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-11-15T01:22:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35H10",
      "43A15",
      "58J65",
      "22E65"
    ],
    "keywords": [
      "infinite-dimensional heisenberg groups",
      "subelliptic taylor isomorphism",
      "appropriate finite dimensional projections",
      "heat kernel measure",
      "square integrable holomorphic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.1970G"
    }
  }
}