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Analytic capacity for two segments

Published online by Cambridge University Press:  22 January 2016

Takafumi Murai
Takafumi Murai*
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Nagoya, 464-01, Japan
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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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 122 , June 1991 , pp. 19 - 42
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

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