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Transactions of the American Mathematical Society

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Univalent functions and the Pompeiu problem


Authors: Nicola Garofalo and Fausto Segàla
Journal: Trans. Amer. Math. Soc. 346 (1994), 137-146
MSC: Primary 30E15; Secondary 35N05
DOI: https://doi.org/10.1090/S0002-9947-1994-1250819-4
MathSciNet review: 1250819
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Abstract: In this paper we prove a result on the Pompeiu problem. If the Schwarz function $ \Phi $ of the boundary of a simply-connected domain $ \Omega \subset {\mathbb{R}^2}$ extends meromorphically into a certain portion $ E$ of $ \Omega $ with a pole at some point $ {z_0} \in E$, then $ \Omega $ has the Pompeiu property unless $ \Phi $ is a Möbius transformation, in which case $ \Omega $ is a disk.


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DOI: https://doi.org/10.1090/S0002-9947-1994-1250819-4
Article copyright: © Copyright 1994 American Mathematical Society

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