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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Testing analyticity on rotation invariant families of curves


Author: Josip Globevnik
Journal: Trans. Amer. Math. Soc. 306 (1988), 401-410
MSC: Primary 30E25; Secondary 30C99, 42C99
DOI: https://doi.org/10.1090/S0002-9947-1988-0927697-0
MathSciNet review: 927697
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Abstract: Let $\Gamma \subset C$ be a piecewise smooth Jordan curve, symmetric with respect to the real axis, which contains the origin in its interior and which is not a circle centered at the origin. Let $\Omega$ be the annulus obtained by rotating $\Gamma$ around the origin. We characterize the curves $\Gamma$ with the property that if $f \in C(\Omega )$ is analytic on $s\Gamma$ for every $s$, $|s| = 1$, then $f$ is analytic in Int $\Omega$.


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Article copyright: © Copyright 1988 American Mathematical Society