Converse of the Maximum Modulus Theorem and Rings of Continuous Complex Functions
Converse of the Maximum Modulus Theorem and Rings of Continuous Complex Functions
It is shown among others that if D is a region (öpen connected set) in the complex plane and C(D) the algehra of continuous complex functions on Dwith the property that for every m em ber/c C (D) and every closed disc M7 in D, ||/||^ r = ||/ ||g ^ then any two such regions are conformally equivalent. Moreover ev ery /is analytic.
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- Communications, Series A1:Mathematics and Statistics