{
  "abstract": "This article concerns Garding Dirichlet operators, and also the theory of Garding polynomials. Garding Dirichlet operators are those which arise from homogeneous polynomials on the space S(n) of symmetric $n \\times n$ polynomials, which are hyperbolic with respect to any positive definite matrix. (In particular, any polynomial on ${\\mathbb R}^n$, which is hyperbolic with respect to elements in $({\\mathbb R_+})^n$, gives rise to a Garding operator on S(n), in many ways.) Here a new duality theorem is developed with many special cases and examples. The dual $g^*$ of a Garding operator $g$ is used to prove a new basic inequality for $g$. An important Lemma of Guo-Phong-Tong is improved upon as a final application.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28773",
  "author_total": 2,
  "authors": [
    {
      "name": "F. Reese Harvey"
    },
    {
      "name": "H. Blaine Lawson Jr"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fr6nagp5t058r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28773",
  "fulltext_url": null,
  "id": "fr6nagp5t058r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28773",
  "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.AP"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7214309991",
  "pdf_url": "https://arxiv.org/pdf/2609.28773",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fr6nagp5t058r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28773",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28773"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Duality for Garding operators and a new inequality of GM/AM type",
  "title_text": "Duality for Garding operators and a new inequality of GM/AM type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/fr6nagp5t058r",
  "venue": "arXiv",
  "versions": []
}