{
  "id": "2201.11565",
  "version": "v1",
  "published": "2022-01-27T15:13:47.000Z",
  "updated": "2022-01-27T15:13:47.000Z",
  "title": "The Hadwiger theorem on convex functions. IV",
  "authors": [
    "Andrea Colesanti",
    "Monika Ludwig",
    "Fabian Mussnig"
  ],
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "New proofs of the Hadwiger theorem for smooth and for general valuations on convex functions are obtained, and the Klain-Schneider theorem on convex functions is established. In addition, an extension theorem for valuations defined on functions with lower dimensional domains is proved and its connection to the Abel transform is explained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-27T15:13:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B45",
      "26B25",
      "49Q20",
      "52A41",
      "52A39"
    ],
    "keywords": [
      "convex functions",
      "hadwiger theorem",
      "lower dimensional domains",
      "abel transform",
      "general valuations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}