The role of Fourier modes in extension theorems of Hartogs-Chirka type
Abstract
We generalize Chirka's theorem on the extension of functions holomorphic in a neighbourhood of graph(F)(∂ D× D) -- where D is the open unit disc and graph(F) denotes the graph of a continuous D-valued function F -- to the bidisc. We extend holomorphic functions by applying the Kontinuitaetssatz to certain continuous families of analytic annuli, which is a procedure suited to configurations not covered by Chirka's theorem.
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