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Symmetry and uniform approximation by analytic functions


Author: Dmitry Khavinson
Journal: Proc. Amer. Math. Soc. 101 (1987), 475-483
MSC: Primary 30E10
DOI: https://doi.org/10.1090/S0002-9939-1987-0908652-8
MathSciNet review: 908652
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Abstract: In this paper we treat the problem of finding all the domains in $ {\mathbf{C}}$ for which the uniform distance from the function $ \bar z$ to the space of analytic functions is equal precisely to (2 area/perimeter). We show that for simply connected domains it occurs if and only if the domain is a disk. We also discuss the relation of the above problem to certain types of symmetry in potential theory and to the theory of Schwarz functions.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0908652-8
Article copyright: © Copyright 1987 American Mathematical Society

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