{
  "abstract": "We study the growth of the spectral function of the Laplace-Beltrami operator on a Riemannian manifold $M$ of dimension $n$. For $n\\geq 3$ we show that for any $x\\in M$ there is a full measure subset $Z_x\\subset M$ such that for all $y\\in Z_x$ \\[E_Λ(x,y) = O_{M,x,y,\\varepsilon}(Λ^{n/2}(\\logΛ)^{3/2}(\\log\\logΛ)^{1/2+\\varepsilon}). \\] For $n=2$ we prove a stronger statement. For any $x\\in M$ there is a full measure subset $Z_x\\subset M$ such that for all $y\\in Z_x$ \\[E_Λ(x,y) = O_{M,x,y,\\varepsilon}(Λ^{5/6}(\\logΛ)^{1/6}(\\log\\logΛ)^{1/6+\\varepsilon}) .\\]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33957",
  "author_total": 1,
  "authors": [
    {
      "name": "Panagiotis Dimakis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9j2vd7xszr1hr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33957",
  "fulltext_url": null,
  "id": "9j2vd7xszr1hr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33957",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214787361",
  "pdf_url": "https://arxiv.org/pdf/2609.33957",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9j2vd7xszr1hr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33957",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33957"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Off-diagonal bounds for spectral projector kernels",
  "title_text": "Off-diagonal bounds for spectral projector kernels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/9j2vd7xszr1hr",
  "venue": "arXiv",
  "versions": []
}