Mathematische Zeitschrift

, Volume 249, Issue 4, pp 883–901 | Cite as

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

  • David E. Barrett
  • Gautam BharaliEmail author


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.


Holomorphic Function Unit Disc Open Unit Extension Theorem Fourier Mode 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Michigan, 525 East UniversityAnn Arbor

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