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 for which the uniform distance from the function 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