{
  "abstract": "This paper studies resolvent expansions at all four spectral thresholds for the discrete Schrödinger operator $H=-Δ+V $ on $\\Z^3$, where $Δ$ denotes the discrete Laplacian on $\\mathbb{Z}^3$ and $V(n)$ is a real-valued decaying potential of $\\mathbb{Z}^3$. At the thresholds 0, 4, 8, and 12, we first give a complete classification of the threshold types and derive the corresponding resolvent expansions in weighted $\\ell^2$-spaces, including the non-generic cases of resonances and eigenvalues. As a result, we establish the Jensen-Kato type time-decay estimates of the evolution $e^{itH} P_{ac}(H)$ to discrete Schrödinger equations with thresholds singularities on $\\Z^3$, with decay $O(t^{-3/2})$ when all thresholds are regular and $O(t^{-1/2})$ otherwise. These results provide a three-dimensional lattice analogue of the Jensen--Kato classical analysis at zero energy threshold on $\\mathbb{R}^3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19845",
  "author_total": 3,
  "authors": [
    {
      "name": "Yanhong Chen"
    },
    {
      "name": "Sisi Huang"
    },
    {
      "name": "Xiaohua Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fgt5tfak6wcgy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19845",
  "fulltext_url": null,
  "id": "fgt5tfak6wcgy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19845",
  "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"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7222280940",
  "pdf_url": "https://arxiv.org/pdf/2610.19845",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fgt5tfak6wcgy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19845",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19845"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Resolvent Expansions at All Spectral Thresholds for Three-Dimensional Discrete Schrödinger Operators",
  "title_text": "Resolvent Expansions at All Spectral Thresholds for Three-Dimensional Discrete Schrödinger Operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/fgt5tfak6wcgy",
  "venue": "arXiv",
  "versions": []
}