The pluripolar hull of a graph and fine analytic continuation
2006 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 44, no 1, 39-60 p.Article in journal (Refereed) Published
We show that if the graph of an analytic function in the unit disk D is not complete pluripolar in C-2 then the projection of its pluripolar hull contains a fine neighborhood of a point p is an element of partial derivative D. 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 T which is defined on a fine neighborhood of a point p is an element of partial derivative D 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-infinity functions on the closed unit disk which are nowhere analytically extendible and have infinitely-sheeted pluripolar hulls. Previous examples of functions with non-trivial pluripolar hull of the graph have fine analytic continuation.
Place, publisher, year, edition, pages
2006. Vol. 44, no 1, 39-60 p.
IdentifiersURN: urn:nbn:se:uu:diva-93258DOI: 10.1007/s11512-005-0004-3ISI: 000240662300003OAI: oai:DiVA.org:uu-93258DiVA: diva2:166687