{
  "abstract": "Let $S\\subset\\Bbb R_+^n$ be compact and convex with $0\\in S$, and let $\\mathcal{P}^S$ be the algebra spanned by monomials with exponents in $\\bigcup_{m\\ge0}(mS\\cap\\Bbb N_0^n)$. We define the associated polynomial hull and prove a Kallin lemma for the union of two sets convex with respect to this algebra. A weighted approximation lemma then shows that, under a sector or ray condition, two admissible monomials generate exactly the functions of the unrestricted algebra that are constant on a specified zero fibre. Applications include an exact density criterion for mixed monomials, a transfer principle for relative perturbations, and density and hull computations on stars of totally real discs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32025",
  "author_total": 2,
  "authors": [
    {
      "name": "Kieu Phuong Chi"
    },
    {
      "name": "Duong Thi Thuy Van"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7np1e3en2qk4m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32025",
  "fulltext_url": null,
  "id": "7np1e3en2qk4m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32025",
  "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.CV"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7223681356",
  "pdf_url": "https://arxiv.org/pdf/2610.32025",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7np1e3en2qk4m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32025",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32025"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Kallin's lemma for polynomials with exponents in a compact convex set and local approximation",
  "title_text": "A Kallin's lemma for polynomials with exponents in a compact convex set and local approximation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/7np1e3en2qk4m",
  "venue": "arXiv",
  "versions": []
}