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Transactions of the American Mathematical Society

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

 
 

 

Analyticity on rotation invariant families of curves


Author: Josip Globevnik
Journal: Trans. Amer. Math. Soc. 280 (1983), 247-254
MSC: Primary 30E05; Secondary 30E20
DOI: https://doi.org/10.1090/S0002-9947-1983-0712259-6
MathSciNet review: 712259
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Abstract: Let $ \mathfrak{G}$ be a rotation invariant family of smooth Jordan curves contained in $ \Delta $, the open unit disc in $ {\mathbf{C}}$. For each $ \Gamma \in \mathfrak{G}$ let $ {D_\Gamma }$ be the simply connected domain bounded by $ \Gamma $. We present various conditions which imply that if $ f$ is a continuous function on $ \Delta $ such that for every $ \Gamma \in \mathfrak{G}$ the function $ f\vert\Gamma $ has a continuous extension to $ \overline {{D_\Gamma }} $ which is analytic in $ {D_\Gamma }$, then $ f$ is analytic in $ \Delta $.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0712259-6
Article copyright: © Copyright 1983 American Mathematical Society

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