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Parametric representation and asymptotic starlikeness in $\mathbb {C}^n$
2008
Proceedings of the American Mathematical Society
In this paper we consider the notion of asymptotic starlikeness in the Euclidean space C n . In the case of the maximum norm, asymptotic starlikeness was introduced by Poreda. We have modified his definition slightly, adding a boundedness condition. We prove that the notion of parametric representation which arises in Loewner theory can be characterized in terms of asymptotic starlikeness; i.e. they are equivalent notions. (A regularity assumption of Poreda is not needed.) In particular,
doi:10.1090/s0002-9939-08-09392-1
fatcat:ph3qz3dhufh6jdj47niwqtk764