Toshiyuki SUGAWA
A self-duality of strong starlikeness
Abstract
In this note, we will show that a simply
connected bounded domain $D$ is strongly
starlike of order $\alpha<1$ if and only
if so is $D^\vee,$ where $D^v$ is the
analytic inversion of the exterior of $D,$
namely, $D^v=\{w\in\mathbb{C}:\, 1/w\in\widehat{\mathbb{C}}
\setminus\bar D\}.$ This fact neatly explains
the relationship between some known properties
of strongly starlike domains and provides
several new characterizations for those domains.
submission: January 28, 2000
revision: February 3, 2000
revision: June 1, 2001
revision: November 22, 2001
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