{
  "id": "2005.08885",
  "version": "v1",
  "published": "2020-05-18T16:56:06.000Z",
  "updated": "2020-05-18T16:56:06.000Z",
  "title": "Lacunary polynomials in $L^1$: geometry of the unit sphere",
  "authors": [
    "Konstantin M. Dyakonov"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA",
    "math.CA",
    "math.CV"
  ],
  "abstract": "Let $\\Lambda$ be a finite set of nonnegative integers, and let $\\mathcal P(\\Lambda)$ be the linear hull of the monomials $z^k$ with $k\\in\\Lambda$, viewed as a subspace of $L^1$ on the unit circle. We characterize the extreme and exposed points of the unit ball in $\\mathcal P(\\Lambda)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-18T16:56:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C10",
      "30H10",
      "42A05",
      "46A55"
    ],
    "keywords": [
      "unit sphere",
      "lacunary polynomials",
      "finite set",
      "linear hull",
      "unit circle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}