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Miklos Schweitzer 1979_9

Source: absolutely convergent of series of holomorphic functions

January 28, 2009
complex analysisfunctioncomplex analysis unsolved

Problem Statement

Let us assume that the series of holomorphic functions ∑k=1∞fk(z) \sum_{k=1}^{\infty}f_k(z) is absolutely convergent for all z∈C z \in \mathbb{C}. Let H⊆C H \subseteq \mathbb{C} be the set of those points where the above sum funcion is not regular. Prove that H H is nowhere dense but not necessarily countable. L. Kerchy
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