{
  "id": "1508.07615",
  "version": "v1",
  "published": "2015-08-30T18:48:21.000Z",
  "updated": "2015-08-30T18:48:21.000Z",
  "title": "Positivity and Fourier integrals over regular hexagon",
  "authors": [
    "Yuan Xu"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $f \\in L^1(\\mathbb{R}^2)$ and let $\\widehat f$ be its Fourier integral. We study summability of the partial integral $S_{\\rho,\\mathsf{H}}(x)=\\int_{\\{\\|y\\|_\\mathsf{H} \\le \\rho\\}} e^{i x\\cdot y}\\widehat f(y) dy$, where $\\|y\\|_\\mathsf{H}$ denotes the uniform norm taken over the regular hexagonal domain. We prove that the Riesz $(R,\\delta)$ means of the inverse Fourier integrals are nonnegative if and if $\\delta \\ge 2$. Moreover, we describe a class of $\\|\\cdot\\|_\\mathsf{H}$-radial functions that are positive definite on $\\mathbb{R}^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-30T18:48:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B08",
      "41A25",
      "41A63"
    ],
    "keywords": [
      "positivity",
      "inverse fourier integrals",
      "regular hexagonal domain",
      "uniform norm taken",
      "partial integral"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}