{
  "abstract": "Let $Ω\\subset\\mathbb Z^d$ be finite and let $S\\subset\\mathbb T^d$ be measurable. We study the discrete Fourier concentration operator \\[ T_{Ω,S}=P_ΩB_SP_Ω, \\] which describes simultaneous localization to a finite set of spatial indices and a prescribed spectral region. For independent exponents $γ,η\\in(0,1]$, we introduce translation seminorms for $Ω$ and $S$ and use them to bound the trace defect \\[ \\operatorname{tr}(T_{Ω,S}-T_{Ω,S}^2). \\] The proof combines an exact trace-defect identity with dyadic Fourier estimates, leading to three regimes: when $γ=η$, the contributions from the dyadic scales are of the same order, and their sum produces a logarithmic factor, while for $γ\\neη$ the sum is controlled by one end of the scale range. For discretizations $$ Ω_R=(RF)\\cap\\mathbb Z^d $$ of a bounded measurable set $F\\subset\\mathbb R^d$ satisfying an upper Minkowski-neighborhood estimate with exponent $γ$, we obtain trace-defect bounds of order $R^{d-γ}\\log R$ in the critical case and $R^{d-\\min\\{γ,η\\}}$ off the critical line. These estimates yield quantitative eigenvalue-counting and plunge-region bounds and recover the discrete Landau asymptotic. For a box model at $γ=η=1$, the logarithmic factor is sharp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12226",
  "author_total": 1,
  "authors": [
    {
      "name": "Azita Mayeli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a3z8shmvppry9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12226",
  "fulltext_url": null,
  "id": "a3z8shmvppry9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12226",
  "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.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7212931282",
  "pdf_url": "https://arxiv.org/pdf/2609.12226",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a3z8shmvppry9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12226",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12226"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Trace-defect bounds for discrete Fourier concentration operators",
  "title_text": "Trace-defect bounds for discrete Fourier concentration operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/a3z8shmvppry9",
  "venue": "arXiv",
  "versions": []
}