{
  "id": "1912.01836",
  "version": "v1",
  "published": "2019-12-04T07:49:55.000Z",
  "updated": "2019-12-04T07:49:55.000Z",
  "title": "Fourier transforms, fractional derivatives, and a little bit of quantum mechanics",
  "authors": [
    "FAbio Bagarello"
  ],
  "comment": "Accepted for publication in Rocky Mountain Journal of Mathematics",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\\Sc(\\mathbb R)$, and then we extend it to its dual set, $\\Sc'(\\mathbb R)$, the set of tempered distributions, provided they satisfy some mild conditions. We discuss some examples, and we show how our definition can be used in a quantum mechanical context.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-04T07:49:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fourier transforms",
      "fractional derivative",
      "little bit",
      "quantum mechanics",
      "test functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}