{
  "id": "2009.03702",
  "version": "v1",
  "published": "2020-09-08T12:45:01.000Z",
  "updated": "2020-09-08T12:45:01.000Z",
  "title": "The Hadwiger theorem on convex functions. I",
  "authors": [
    "Andrea Colesanti",
    "Monika Ludwig",
    "Fabian Mussnig"
  ],
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on ${\\mathbb R}^n$ is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-08T12:45:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B45",
      "26B25",
      "49Q20",
      "52A41",
      "52A39"
    ],
    "keywords": [
      "hadwiger theorem",
      "singular hessian valuations",
      "rotation invariant valuations",
      "classical intrinsic volumes",
      "functional versions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}