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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.

Information

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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