Holomorphic extendability in $\mathbf C^n$ as a rare phenomenon
Complex Variables
2016-12-02 v2 Classical Analysis and ODEs
Functional Analysis
Abstract
We consider various notions of holomorphic extendability of complex valued functions defined on subsets of , including one-sided extendability. We show that in the relevant function spaces, these phenomena of holomorphic extendability are rare in the topological sense, generalizing several results of the article "One sided extendability and -continuous analytic capacities" by E. Bolkas, V. Nestoridis, C. Panagiotis and M. Papadimitrakis, in dimensions .
Cite
@article{arxiv.1611.05367,
title = {Holomorphic extendability in $\mathbf C^n$ as a rare phenomenon},
author = {Nikolaos Georgakopoulos},
journal= {arXiv preprint arXiv:1611.05367},
year = {2016}
}
Comments
15 pages. Revision: Corrected some remarks on the one dimensional case and revised the star condition of section 2. Other minor revisions and corrections