The pluripolar hull of a graph and fine analytic continuation

• Autores: Tomas Edlund, Burglind Jöricke
• Localización: Arkiv för matematik, ISSN 0004-2080, Vol. 44, Nº 1, 2006, págs. 39-60
• Idioma: inglés
• DOI: 10.1007/s11512-005-0004-3
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• Resumen

  • We show that if the graph of an analytic function in the unit disk D is not complete pluripolar in C2 then the projection of its pluripolar hull contains a fine neighborhood of a point p�¸�ÝD. Moreover the projection of the pluripolar hull is always finely open. On the other hand we show that if an analytic function f in D extends to a function F which is defined on a fine neighborhood of a point p�¸�ÝD and is finely analytic at p then the pluripolar hull of the graph of f contains the graph of F over a smaller fine neighborhood of p. We give several examples of functions with this property of fine analytic continuation. As a corollary we obtain new classes of analytic functions in the disk which have non-trivial pluripolar hulls, among them C�� functions on the closed unit disk which are nowhere analytically extendible and have infinitelysheeted pluripolar hulls. Previous examples of functions with non-trivial pluripolar hull of the graph have fine analytic continuation.