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Analytic capacity for two segments
Published online by Cambridge University Press: 22 January 2016
Extract
The analytic capacity γ(E) of a compact set E in the complex plane C is defined by γ(E) = sup , where — f′(∞) is the 1/z-coeffieient of f(ζ) at infinity and the supremum is taken over all bounded analytic functions f(ζ) outside E with supremum norm less than or equal to 1. Analytic capacity γ(·) plays various important roles in the theory of bounded analytic functions.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1991
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