, Volume 249, Issue 4, pp 883-901
Date: 21 Oct 2004

The role of Fourier modes in extension theorems of Hartogs-Chirka type

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Abstract.

We generalize Chirka’s theorem on the extension of functions holomorphic in a neighbourhood of Γ(F)∪(∂D×D) – where D is the open unit disc and Γ(F) is the graph of a continuous D-valued function F – to the bidisc. We extend holomorphic functions by applying the Kontinuitätssatz to certain continuous families of analytic annuli, which is a procedure suited to configurations not covered by Chirka’s theorem.

Mathematics Subject classification (2000): 32D15
Work supported by NSF Grant DMS-0072237.