{
  "abstract": "Laplace--King representations combine spherical harmonics with King functions [Wang et al., Chin. Phys. B \\textbf{34}, 065201 (2025)], the radial kernels of shifted isotropic Gaussians. The radial parameters may vary across angular modes. We prove that, for every angular degree, fixed-width kernels with positive real shifts have dense complex linear span in a Gaussian-weighted radial \\(L^2\\) space. Finite Laplace--King representations are dense in the corresponding three-dimensional weighted space; allowing variable widths preserves density in the same reference norm. A generating identity connects the kernels to generalized Laguerre polynomials. The self-adjoint King operator is unitarily equivalent to the free radial Schrödinger operator; its spectral resolution defines a continuous King mixture model (KMM) through imaginary-shift kernels in a distinct weighted Hilbert space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.12455",
  "author_total": 2,
  "authors": [
    {
      "name": "Yanpeng Wang"
    },
    {
      "name": "Zhe Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3bae0p7z6zkrb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.12455",
  "fulltext_url": null,
  "id": "3bae0p7z6zkrb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.12455",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "arxiv",
      "physics.plasm-ph"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7164581803",
  "pdf_url": "https://arxiv.org/pdf/2606.12455",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3bae0p7z6zkrb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2606.12455",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.12455"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.plasm-ph",
      "subfield": "plasma"
    }
  ],
  "title": "Laplace--King representations: density and spectral theory",
  "title_text": "Laplace--King representations: density and spectral theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/3bae0p7z6zkrb",
  "venue": "arXiv",
  "versions": []
}