{
  "id": "math/0311238",
  "version": "v1",
  "published": "2003-11-14T08:34:17.000Z",
  "updated": "2003-11-14T08:34:17.000Z",
  "title": "Analyticity on families of circles",
  "authors": [
    "Josip Globevnik"
  ],
  "categories": [
    "math.CV"
  ],
  "abstract": "It is known that if f is a continuous function on the complex plane which extends holomorphically from each circle surrounding the origin then f is not necessarily holomorphic. In the paper we prove that if, in addition, f extends holomorphically from each circle belonging to an open family of circles which do not surround the origin then f is holomorphic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-14T08:34:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "analyticity",
      "complex plane",
      "necessarily holomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11238G"
    }
  }
}