{
  "abstract": "For a given function $f$ on a discrete subspace $Γ$ of a noncompact Riemannian symmetric space $G/K$, we construct analytic, noncompactly supported functions $W$ on $G/K$ with $W|_Γ=f$ that, in addition, satisfy an invariant differential equation on $G/K$. The key step is to regard $W$ as an orthogonal projection onto a space of coherent states in a representation of the Lie group $G$ in a Hilbert space that admits a strictly positive definite reproducing kernel. The techniques are implemented for the heat kernel on $G/K$, and $W$ is expressed in terms of certain closed formulas for linearly independent coherent states.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03167",
  "author_total": 1,
  "authors": [
    {
      "name": "Peter Vang Uttenthal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8rafrr14njg3t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03167",
  "fulltext_url": null,
  "id": "8rafrr14njg3t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03167",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7208707067",
  "pdf_url": "https://arxiv.org/pdf/2609.03167",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8rafrr14njg3t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03167",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03167"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Positive kernels in Lie group representations and Fourier interpolation",
  "title_text": "Positive kernels in Lie group representations and Fourier interpolation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/8rafrr14njg3t",
  "venue": "arXiv",
  "versions": []
}