{
  "id": "1209.1799",
  "version": "v1",
  "published": "2012-09-09T13:40:02.000Z",
  "updated": "2012-09-09T13:40:02.000Z",
  "title": "A class of index transforms generated by the Mellin and Laplace operators",
  "authors": [
    "Semyon Yakubovich"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Classical integral representation of the Mellin type kernel in terms of the Laplace integral gives an idea to construct a new class of non-convolution (index) transforms. Particular examples give the Kontorovich-Lebedev-like transformation and new transformations with hypergeometric functions as kernels. Mapping properties and inversion formulas are obtained. Finally we prove a new inversion theorem for the modified Kontorovich-Lebedev transform",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-09T13:40:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "44A15",
      "33C05",
      "33C10",
      "33C15"
    ],
    "keywords": [
      "index transforms",
      "laplace operators",
      "mellin type kernel",
      "integral representation",
      "laplace integral"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.1799Y"
    }
  }
}