{
  "id": "0811.3103",
  "version": "v1",
  "published": "2008-11-19T12:47:34.000Z",
  "updated": "2008-11-19T12:47:34.000Z",
  "title": "Decompositions, approximate structure, transference, and the Hahn-Banach theorem",
  "authors": [
    "W. T. Gowers"
  ],
  "comment": "48 pages",
  "doi": "10.1112/blms/bdq018",
  "categories": [
    "math.CO",
    "math.FA"
  ],
  "abstract": "This paper is partly a survey of certain kinds of results and proofs in additive combinatorics, and partly a discussion of how useful the finite-dimensional Hahn-Banach theorem can be. The most interesting single result is probably a simpler proof of a key step in the proof of the Green-Tao theorem, but several other applications of the method are given. A similarly simplified proof of the Green-Tao transference principle was obtained independently (and expressed in a rather different language) by Reingold, Trevisan, Tulsiani and Vadhan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-19T12:47:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D99"
    ],
    "keywords": [
      "approximate structure",
      "decompositions",
      "green-tao transference principle",
      "finite-dimensional hahn-banach theorem",
      "green-tao theorem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.3103G"
    }
  }
}