Nikolaos Georgakopoulos

arXiv2016

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

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 $n\ge 2$.

math.CV↗

arXiv2016

Extensions of the Laurent Decomposition and the spaces $A^p(Ω)$

We generalize the classical Laurent decomposition in the setting of domains $Ω\subseteq \mathbb C$ bounded by Jordan curves. This leads us to study the Fréchet spaces $A^p(Ω)$, and their relation to the spaces $C^p(\partial Ω)$. In the final section, we examine the case of a non Jordan domain $Ω$.

math.CV↗