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Analytic on C excluding countably many points

Source: IMS 2009

May 20, 2009
functionalgebradomaincalculusintegrationtopologyFunctional Analysis

Problem Statement

Let AC A\subset \mathbb C be a closed and countable set. Prove that if the analytic function f:C\AC f: \mathbb C\backslash A\longrightarrow \mathbb C is bounded, then f f is constant.