Univalent functions and the Pompeiu problem
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- by Nicola Garofalo and Fausto Segàla PDF
- Trans. Amer. Math. Soc. 346 (1994), 137-146 Request permission
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.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- 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