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This monograph offers a deep dive into the boundary properties of analytic functions, extending classical results beyond the unit disk and finitely connected domains. The primary goal is to describe and study classes of domains of arbitrary connectivity, generalizing key theorems from complex analysis.
Within these various domain types, the work explores several critical questions. These include describing the modulus of boundary values for specific function classes, analyzing the properties of limit sets, and establishing a generalized maximum principle. The text also investigates the boundary behavior of extremal functions, explores the duality of Hardy classes, and addresses other related issues concerning the boundary properties of analytic functions.
This academic work is ideal for researchers and graduate students specializing in complex analysis, particularly those focused on function theory in multiply connected domains. It provides a rigorous treatment of advanced topics, bridging the gap between classical theory and modern generalizations.