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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
Article

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.

Keywords

Holomorphic Function Unit Disc Open Unit Extension Theorem Fourier Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

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

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