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 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.