{
  "id": "1803.02459",
  "version": "v1",
  "published": "2018-03-06T22:45:22.000Z",
  "updated": "2018-03-06T22:45:22.000Z",
  "title": "Complex Hyperbolic Geometry and Hilbert Spaces with the Complete Pick Property",
  "authors": [
    "Richard Rochberg"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Suppose $H$ is a finite dimensional reproducing kernel Hilbert space of functions on $X.$ If $H$ has the complete Pick property then there is an isometric map, $\\Phi,$ from $X,$ with the metric induced by $H,$ into complex hyperbolic space, $\\mathbb{CH}^{n},$ with its pseudohyperbolic metric. We investigate the relationships between the geometry of $\\Phi(X)$ and the function theory of $H$ and its multiplier algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-06T22:45:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E22",
      "51M10",
      "52B11"
    ],
    "keywords": [
      "complete pick property",
      "complex hyperbolic geometry",
      "finite dimensional reproducing kernel hilbert",
      "dimensional reproducing kernel hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}