{
  "id": "0903.1097",
  "version": "v3",
  "published": "2009-03-06T05:04:03.000Z",
  "updated": "2014-03-23T11:24:51.000Z",
  "title": "Fourier transform of the additive group in algebraically closed valued fields",
  "authors": [
    "Yimu Yin"
  ],
  "categories": [
    "math.LO",
    "math.AG"
  ],
  "abstract": "We continue the study of the Hrushovski-Kazhdan integration theory and consider exponential integrals. The Grothendieck ring is enlarged via a tautological additive character and hence can receive such integrals. We then define the Fourier transform in our integration theory and establish some fundamental properties of it. Thereafter a basic theory of distributions is also developed. We construct the Weil representations in the end as an application. The results are completely parallel to the classical ones.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-23T11:24:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60",
      "11S80",
      "20C08"
    ],
    "keywords": [
      "algebraically closed valued fields",
      "fourier transform",
      "additive group",
      "hrushovski-kazhdan integration theory",
      "exponential integrals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.1097Y"
    }
  }
}