Pluripolar hulls and fine holomorphy

Authors :: Wiegerinck, Jan
Source :: Indagationes Mathematicae. 34:248-258
Publication Year :: 2023
Publisher :: Elsevier BV, 2023.
Abstract: Examples by Poletsky and the author and by Zwonek show the existence nowhere extendable holomorphic functions with the property that the pluripolar hull of their graphs is much larger than the graph of the respective functions and contains multiple sheets. We will explain this phenomenon by fine analytic continuation of the function over part of a Cantor-type set involved. This gives more information on the hull, and allows for weakening and effectiveness of the conditions in the original examples.<br />Comment: 12 pages. In version 2 quite some annoying typo's and mistakes were corrected. In version 3 a serious gap has been filled