{
  "id": "1912.11219",
  "version": "v1",
  "published": "2019-12-24T06:08:46.000Z",
  "updated": "2019-12-24T06:08:46.000Z",
  "title": "Anti-uniformity norms, anti-uniformity functions and their algebras on Euclidean spaces",
  "authors": [
    "A. Martina Neuman"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $k\\geq 2$ be an integer. Given a uniform function $f$ - one that satisfies $\\|f\\|_{U(k)}<\\infty$, there is an associated anti-uniform function $g$ - one that satisfied $\\|g\\|_{U(k)}^{*}$. The question is, can one approximate $g$ with the Gowers-Host-Kra dual function $D_{k}f$ of $f$? Moreover, given the generalized cubic convolution products $D_{k}(f_{\\alpha}:\\alpha\\in\\tilde{V}_{k})$, what sorts of algebras can they form? In short, this paper explores possible structures of anti-uniformity on Euclidean spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-24T06:08:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "euclidean spaces",
      "anti-uniformity norms",
      "anti-uniformity functions",
      "gowers-host-kra dual function",
      "generalized cubic convolution products"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}