{
  "id": "1605.08089",
  "version": "v1",
  "published": "2016-05-25T22:01:37.000Z",
  "updated": "2016-05-25T22:01:37.000Z",
  "title": "Fourier transforms of powers of well-behaved 2D real analytic functions",
  "authors": [
    "Michael Greenblatt"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "This paper is a companion paper to [G4], where sharp estimates are proven for Fourier transforms of compactly supported functions built out of two-dimensional real-analytic functions. The theorems of [G4] are stated in a rather general form. In this paper, we expand on the results of [G4] and show that there is a class of \"well-behaved\" functions that contains a number of relevant examples for which such estimates can be explicitly described in terms of the Newton polygon of the function. We will further see that for a subclass of these functions, one can prove noticeably more precise estimates, again in an explicitly describable way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-25T22:01:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20"
    ],
    "keywords": [
      "well-behaved 2d real analytic functions",
      "fourier transforms",
      "two-dimensional real-analytic functions",
      "sharp estimates",
      "companion paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}