Holomorphic extendability in \mathbf Cⁿ as a rare phenomenon

2016/11/16 by Georgakopoulos, Nikolaos
#Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1611.05367

Abstract

We consider various notions of holomorphic extendability of complex valued functions defined on subsets of \mathbf Cⁿ, 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≥ 2.

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