Holomorphic extendability in ${\mathbf{C}}^n$ as a rare phenomenon

Abstract

We consider various notions of holomorphic extendability of complex valued functions defined on subsets of ${\mathbf{C}}^n$, 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 $p$-continuous analytic capacities" by E. Bolkas, V. Nestoridis, C. Panagiotis and M. Papadimitrakis, in dimensions $n\ge 2$.

15 pages. Revision: Corrected some remarks on the one dimensional case and revised the star condition of section 2. Other minor revisions and corrections

References in corpus (2)

• One sided extendability and p-continuous analytic capacities
• Universal Taylor Series On Convex Subsets Of $\Mathbb{C}^{N}$