{
  "id": "2501.03351",
  "version": "v1",
  "published": "2025-01-06T19:32:46.000Z",
  "updated": "2025-01-06T19:32:46.000Z",
  "title": "Strichartz's conjecture for the spinor bundle over the real hyperbolic space",
  "authors": [
    "Abdelhamid Boussejra",
    "Khalid Koufany"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2406.00536",
  "categories": [
    "math.RT",
    "math.DG"
  ],
  "abstract": "Let $H^n(\\mathbb R)$ denote the real hyperbolic space realized as the symmetric space $Spin_0(1,n)/Spin(n)$. In this paper, we provide a characterization for the image of the Poisson transform for $L^2$-sections of the spinor bundle over the boundary ${\\partial H}^n(\\mathbb R)$. As a consequence, we obtain an $L^2$ uniform estimate for the generalized spectral projections associated to the spinor bundle over $H^n(\\mathbb R)$, thereby extending Strichartz's conjecture from the scalar case to the spinor setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-06T19:32:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A90",
      "43A85",
      "58J50",
      "15A66"
    ],
    "keywords": [
      "real hyperbolic space",
      "spinor bundle",
      "symmetric space",
      "poisson transform",
      "uniform estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}