{
  "id": "1410.3674",
  "version": "v1",
  "published": "2014-10-14T12:53:02.000Z",
  "updated": "2014-10-14T12:53:02.000Z",
  "title": "Spectral types of linear $q$-difference equations and $q$-analog of middle convolution",
  "authors": [
    "Hidetaka Sakai",
    "Masashi Yamaguchi"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We give a $q$-analog of middle convolution for linear $q$-difference equations with rational coefficients. In the differential case, middle convolution is defined by Katz, and he examined properties of middle convolution in detail. In this paper, we define a $q$-analog of middle convolution. Moreover, we show that it also can be expressed as a $q$-analog of Euler transformation. The $q$-middle convolution transforms Fuchsian type equation to Fuchsian type equation and preserves rigidity index of $q$-difference equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-14T12:53:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D15",
      "39A13"
    ],
    "keywords": [
      "difference equations",
      "spectral types",
      "middle convolution transforms fuchsian type",
      "convolution transforms fuchsian type equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.3674S"
    }
  }
}