A self-duality of strong starlikeness

Sugawa, Toshiyuki

Kodai Math. J., Tome 28 (2005) no. 1, p. 382-389 / Harvested from Project Euclid

Résumé

In this note, we will show that a simply connected bounded domain D is strongly starlike of order α < 1 with respect to the origin if and only if so is D^∨, where D^∨ is the analytic inversion of the exterior of D, namely, $D^\vee=\{w\in\mathbb{C}:\, 1/w\in\widehat{\mathbb{C}} \setminus\bar D\}$ . This fact neatly explains the relationship between some known properties of strongly starlike domains and provides several new characterizations for those domains.

Publié le : 2005-06-14
Classification:

@article{1123767018,
     author = {Sugawa, Toshiyuki},
     title = {A self-duality of strong starlikeness},
     journal = {Kodai Math. J.},
     volume = {28},
     number = {1},
     year = {2005},
     pages = { 382-389},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1123767018}
}

Sugawa, Toshiyuki. A self-duality of strong starlikeness. Kodai Math. J., Tome 28 (2005) no. 1, pp.  382-389. http://gdmltest.u-ga.fr/item/1123767018/