{
  "abstract": "We introduce the weighted Laplace space $H_w$, an RKHS of Laplace transforms on $(0,\\infty)$, and study spectral measures in its dual space $H'_w$. For conforming FEM discretizations of the Dirichlet Laplacian on bounded Lipschitz domains, we prove the dual-norm inequality $\\|μ_h\\|_{H'_w} \\leq \\|μ\\|_{H'_w}$, where $μ= \\sum_kδ_{λ_k}$ and $μ_h = \\sum_k δ_{λ_{k,h}}$. The proof combines min-max monotonicity of FEM eigenvalues with a heat-trace representation of the dual norm. We then analyze $H_w$-adapted rational approximation of shifted symbols $ϕ(x)=(x+κ^2)^{-β}$ and give a conditional transfer principle for estimates proved in the corresponding weighted Laplace pre-image norm. Via dual pairing, the norm inequality yields uniform bounds for finite spectral sums and related transformed observables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06243",
  "author_total": 3,
  "authors": [
    {
      "name": "Stefan Jakobsson"
    },
    {
      "name": "Alice Kozakevicius"
    },
    {
      "name": "Stig Larsson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56mprmv00g700.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06243",
  "fulltext_url": null,
  "id": "56mprmv00g700",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06243",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7212020596",
  "pdf_url": "https://arxiv.org/pdf/2609.06243",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56mprmv00g700.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2609.06243",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06243"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Weighted Laplace Spaces for Spectral Measures and Rational Approximation",
  "title_text": "Weighted Laplace Spaces for Spectral Measures and Rational Approximation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/56mprmv00g700",
  "venue": "arXiv",
  "versions": []
}