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

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

2004-05-05

arxiv.org/abs/math/0405077v1

Math. Z. 249 (2005), 883-901

Mathematics

Complex Variables

17 pages

Scientific paper

10.1007/s00209-04-0742-0

We generalize Chirka's theorem on the extension of functions holomorphic in a neighbourhood of graph(F)\cup(\partial D\times 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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