{
  "id": "1802.06657",
  "version": "v1",
  "published": "2018-02-19T14:54:03.000Z",
  "updated": "2018-02-19T14:54:03.000Z",
  "title": "On the product formula and convolution associated with the index Whittaker transform",
  "authors": [
    "Rúben Sousa",
    "Manuel Guerra",
    "Semyon Yakubovich"
  ],
  "comment": "24 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We deduce a product formula for the Whittaker $W$ function whose kernel does not depend on the second parameter. Making use of this formula, we define the positivity-preserving convolution operator associated with the index Whittaker transform, which is seen to be a direct generalization of the Kontorovich-Lebedev convolution. The mapping properties of this convolution operator are investigated; in particular, a Banach algebra property is established and then applied to yield an analogue of the Wiener-L\\'evy theorem for the index Whittaker transform. We show how our results can be used to prove the existence of a unique solution for a class of convolution-type integral equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-19T14:54:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C15",
      "44A15",
      "43A20",
      "45E10"
    ],
    "keywords": [
      "index whittaker transform",
      "product formula",
      "convolution-type integral equations",
      "banach algebra property",
      "unique solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}