{
  "annotation_id": "92b163d2-c863-4c71-878c-8b511ac300fd",
  "date_created": "2026-02-17T05:53:08.894000Z",
  "date_modified": "2026-02-17T05:53:08.894000Z",
  "file_hash": "002750ae8b1cc56ede75b145d4e4cfe206b0c0ccc79f83fea00cdd7e38d59380",
  "private": false,
  "record": {
    "abstract": "We study differentiability conditions on a complex measure $\\nu$ at a point $x_0\\in\\mathbb{R}^d$, in relation with the boundary convergence at that point of the Poisson-type integral $P_t\\nu=e^{-t\\sqrt L}\\nu$, where $L=-\\Delta+|x|^2$ is the Hermite operator. In particular, we show that $x_0$ is a Lebesgue point for $\\nu$ iff a slightly stronger notion than non-tangential convergence holds for $P_t\\nu$ at $x_0$. We also show non-tangential convergence when $x_0$ is a $\\sigma$-point of $\\nu$, a weaker notion than Lebesgue point, which for $d=1$ coincides with the classical Fatou condition.",
    "arxiv_id": "2601.07063",
    "authors": [
      "Guillermo Flores",
      "Gustavo Garrig\u00f3s",
      "Beatriz Viviani"
    ],
    "categories": [
      "math.AP",
      "math.CA"
    ],
    "doi": "10.1007/s00028-025-01079-5",
    "journal_ref": "Journal of Evolution Equations 25, 50 (2025)",
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Lebesgue points of measures and non tangential convergence of Poisson-Hermite integrals",
    "url": "https://arxiv.org/abs/2601.07063",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a899a708-0be5-44a8-a826-35ee022341e7",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}