{
  "abstract": "Let $w \\colon (0,1) \\to \\mathbb{R}_{+}$ be a weight. We prove that for an arbitrary Schauder basis $\\{e^{i λ_n t}\\}_{n \\in \\mathbb{Z}}$ in $L^2(0,1)$ and an arbitrary lacunary defect set $A \\subset \\mathbb{Z}$ the system $\\{w(t) r_n(t)\\}_{n \\in \\mathbb{Z} \\setminus A}$ is always complete and never minimal for any weight $w$ satisfying a natural decay condition, which is sharp on the exponential scale. Moreover, we establish a simple combinatorial criterion for systems of the form $ \\{ w(t) e^{2πi n t} \\}_{n \\in \\mathbb{Z} \\setminus A} $ to be complete and minimal in $L^2(0,1)$ for an arbitrary weight $w$ and a finite defect set $A \\subset \\mathbb{Z}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06114",
  "author_total": 2,
  "authors": [
    {
      "name": "Ivan Arefev"
    },
    {
      "name": "Andrei V. Semenov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/51dhr02pwd79c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06114",
  "fulltext_url": null,
  "id": "51dhr02pwd79c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06114",
  "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.CO"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7220668251",
  "pdf_url": "https://arxiv.org/pdf/2610.06114",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/51dhr02pwd79c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06114",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06114"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Exactness of weighted exponential systems with a defect",
  "title_text": "Exactness of weighted exponential systems with a defect",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/51dhr02pwd79c",
  "venue": "arXiv",
  "versions": []
}