The Pluripolar Hull of a Graph and Fine Analytic Continuation
| dc.creator | Edlund, T. | |
| dc.creator | Joericke, B. | |
| dc.date | 2004-05-03 | |
| dc.date.accessioned | 2026-07-07T05:07:53Z | |
| dc.date.available | 2026-07-07T05:07:53Z | |
| dc.description | We show that if the graph of a bounded analytic function in the unit disk $\mathbb D$ is not complete pluripolar in $\mathbb C^2$ then the projection of the closure of its pluripolar hull contains a fine neighborhood of a point $p \in \partial \mathbb D$. On the other hand we show that if an analytic function $f$ in $\mathbb D$ extends to a function $\mathcal{F}$ which is defined on a fine neighborhood of a point $p \in \partial \mathbb D$ and is finely analytic at $p$ then the pluripolar hull of the graph of $f$ contains the graph of $\mathcal{F}$ 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 $C^\infty$ 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. | |
| dc.identifier | https://arxiv.org/abs/math/0405025 | |
| dc.identifier | http://arxiv.org/abs/math/0405025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71040 | |
| dc.subject | Complex Variables | |
| dc.subject | 32U15 | |
| dc.title | The Pluripolar Hull of a Graph and Fine Analytic Continuation | |
| dc.type | text |