{
  "id": "0809.2806",
  "version": "v1",
  "published": "2008-09-16T20:44:45.000Z",
  "updated": "2008-09-16T20:44:45.000Z",
  "title": "Smooth and weak synthesis of the anti-diagonal in Fourier algebras of Lie groups",
  "authors": [
    "B. Doug Park",
    "Ebrahim Samei"
  ],
  "categories": [
    "math.FA",
    "math.GR"
  ],
  "abstract": "Let $G$ be a Lie group of dimension $n$, and let $A(G)$ be the Fourier algebra of $G$. We show that the anti-diagonal $\\check{\\Delta}_G=\\{(g,g^{-1})\\in G\\times G \\mid g\\in G\\}$ is both a set of local smooth synthesis and a set of local weak synthesis of degree at most $[\\frac{n}{2}]+1$ for $A(G\\times G)$. We achieve this by using the concept of the cone property in \\cite{ludwig-turowska}. For compact $G$, we give an alternative approach to demonstrate the preceding results by applying the ideas developed in \\cite{forrest-samei-spronk}. We also present similar results for sets of the form $HK$, where both $H$ and $K$ are subgroups of $G\\times G\\times G\\times G$ of diagonal forms. Our results very much depend on both the geometric and the algebraic structure of these sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-16T20:44:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A30",
      "43A45"
    ],
    "keywords": [
      "fourier algebra",
      "lie group",
      "anti-diagonal",
      "local smooth synthesis",
      "local weak synthesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.2806P"
    }
  }
}