Symmetry and uniform approximation by analytic functions
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- by Dmitry Khavinson PDF
- Proc. Amer. Math. Soc. 101 (1987), 475-483 Request permission
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.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- 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