The role of Fourier modes in extension theorems of Hartogs-Chirka type
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- Barrett, D. & Bharali, G. Math. Z. (2005) 249: 883. doi:10.1007/s00209-004-0742-0
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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.