{
  "id": "1401.3143",
  "version": "v2",
  "published": "2014-01-14T11:26:05.000Z",
  "updated": "2014-03-10T16:20:37.000Z",
  "title": "New inversion, convolution and Titchmarsh's theorems for the half-Hartley transform",
  "authors": [
    "Semyon Yakubovich"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "The generalized Parseval equality for the Mellin transform is employed to prove the inversion theorem in L_2 with the respective inverse operator related to the Hartley transform on the nonnegative half-axis (the half-Hartley transform). Moreover, involving the convolution method, which is based on the double Mellin-Barnes integrals, the corresponding convolution and Titchmarsh's theorems for the half-Hartley transform are established. As an application, we consider solvability conditions for a homogeneous integral equation of the second kind involving the Hartley kernel.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-10T16:20:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "44A15",
      "44A35",
      "45E05",
      "45E10"
    ],
    "keywords": [
      "half-hartley transform",
      "titchmarshs theorems",
      "generalized parseval equality",
      "second kind",
      "mellin transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.3143Y"
    }
  }
}