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

dvi file(no figures)

PDF file

Back