{
  "id": "1601.01850",
  "version": "v1",
  "published": "2016-01-08T12:22:21.000Z",
  "updated": "2016-01-08T12:22:21.000Z",
  "title": "Integration of Oscillatory and Subanalytic Functions",
  "authors": [
    "Raf Cluckers",
    "Georges Comte",
    "Daniel J. Miller",
    "Jean-Philippe Rolin",
    "Tamara Servi"
  ],
  "categories": [
    "math.AG",
    "math.CA",
    "math.LO"
  ],
  "abstract": "We prove the stability under integration and under Fourier transform of a concrete class of functions containing all globally subanalytic functions and their complex exponentials. This paper extends the investigation started in [J.-M. Lion, J.-P. Rolin: \"Volumes, feuilles de Rolle de feuilletages analytiques et th\\'eor\\`eme de Wilkie\" Ann. Fac. Sci. Toulouse Math. (6) 7 (1998), no. 1, 93-112] and [R. Cluckers, D. J. Miller: \"Stability under integration of sums of products of real globally subanalytic functions and their logarithms\" Duke Math. J. 156 (2011), no. 2, 311-348] to an enriched framework including oscillatory functions. It provides a new example of fruitful interaction between analysis and singularity theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-08T12:22:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B15",
      "14P15",
      "32B20",
      "42B20",
      "42A38",
      "03C64",
      "14P10",
      "33B10"
    ],
    "keywords": [
      "integration",
      "real globally subanalytic functions",
      "complex exponentials",
      "fourier transform",
      "feuilletages analytiques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160101850C"
    }
  }
}