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Transactions of the American Mathematical Society

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Analyticity on translates of a Jordan curve


Author: Josip Globevnik
Journal: Trans. Amer. Math. Soc. 359 (2007), 5555-5565
MSC (2000): Primary 30E20
DOI: https://doi.org/10.1090/S0002-9947-07-04264-X
Published electronically: May 8, 2007
MathSciNet review: 2327042
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Abstract: Let $ \Omega $ be a domain in $ \mathbb{C}$ which is symmetric with respect to the real axis and whose boundary is a real analytic simple closed curve. Translate $ \overline\Omega $ vertically to get $ K = \bigcup\{ \overline\Omega +it, -r\leq t\leq r\}$ where $ r>0$ is such that $ (\overline\Omega -ir)\cap(\overline\Omega +ir)= \emptyset $. We prove that if $ f$ is a continuous function on $ K$ such that for each $ t, -r\leq t\leq r$, the function $ f\vert(b\Omega+it)$ has a continuous extension to $ \overline\Omega +it$ which is holomorphic on $ \Omega +it$, then $ f$ is holomorphic on $ {\rm Int}K$.


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Additional Information

Josip Globevnik
Affiliation: Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Ljubljana, Slovenia
Email: josip.globevnik@fmf.uni-lj.si

DOI: https://doi.org/10.1090/S0002-9947-07-04264-X
Received by editor(s): June 15, 2005
Received by editor(s) in revised form: December 1, 2005
Published electronically: May 8, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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