{
  "id": "2209.03801",
  "version": "v1",
  "published": "2022-09-08T13:21:37.000Z",
  "updated": "2022-09-08T13:21:37.000Z",
  "title": "Infinite-Dimensional Stochastic Transforms and Reproducing Kernel Hilbert space",
  "authors": [
    "Palle E. T. Jorgensen",
    "Myung-Sin Song",
    "James Feng Tian"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "By way of concrete presentations, we construct two infinite-dimensional transforms at the crossroads of Gaussian fields and reproducing kernel Hilbert spaces (RKHS), thus leading to a new infinite-dimensional Fourier transform in a general setting of Gaussian processes. Our results serve to unify existing tools from infinite-dimensional analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-08T13:21:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B32",
      "41A15",
      "41A65",
      "42A82",
      "42C15",
      "46E22",
      "47A05",
      "47N10",
      "60G15",
      "62H25",
      "68T07",
      "81S05",
      "90C20",
      "94A08",
      "94A12",
      "94A20"
    ],
    "keywords": [
      "reproducing kernel hilbert space",
      "infinite-dimensional stochastic transforms",
      "infinite-dimensional fourier transform",
      "gaussian fields",
      "concrete presentations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}