{
  "id": "math/0409100",
  "version": "v1",
  "published": "2004-09-07T08:42:41.000Z",
  "updated": "2004-09-07T08:42:41.000Z",
  "title": "Multiscaled wavelet transforms, ridgelet transforms, and Radon transforms on the space of matrices",
  "authors": [
    "G. Olafsson",
    "E. Ournycheva",
    "B. Rubin"
  ],
  "comment": "29 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $M$ be the space of real $n\\times m$ matrices which can be identified with the Euclidean space $R^{nm}$. We introduce continuous wavelet transforms on $M$ with a multivalued scaling parameter represented by a positive definite symmetric matrix. These transforms agree with the polar decomposition on $M$ and coincide with classical ones in the rank-one case $m=1$. We prove an analog of Calderon's reproducing formula for $L^2$-functions and obtain explicit inversion formulas for the Riesz potentials and Radon transforms on $M$. We also introduce continuous ridgelet transforms associated to matrix planes in $M$. An inversion formula for these transforms follows from that for the Radon transform.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-07T08:42:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C40",
      "44A12"
    ],
    "keywords": [
      "radon transform",
      "multiscaled wavelet transforms",
      "ridgelet transforms",
      "explicit inversion formulas",
      "positive definite symmetric matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9100O"
    }
  }
}