uu.seUppsala University Publications

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The pluripolar hull of a graph and fine analytic continuationPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2006 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 44, no 1, p. 39-60Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2006. Vol. 44, no 1, p. 39-60
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-93258DOI: 10.1007/s11512-005-0004-3ISI: 000240662300003OAI: oai:DiVA.org:uu-93258DiVA, id: diva2:166687
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Available from: 2005-09-01 Created: 2005-09-01 Last updated: 2017-12-14Bibliographically approved
##### In thesis

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.

1. Pluripolar Sets and Pluripolar Hulls$(function(){PrimeFaces.cw("OverlayPanel","overlay166690",{id:"formSmash:j_idt892:0:j_idt899",widgetVar:"overlay166690",target:"formSmash:j_idt892:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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