Illinois Journal of Mathematics

Angular derivatives and semigroups of holomorphic functions

Nikolaos Karamanlis

Abstract

A simply connected domain $\Omega \subset \mathbb{C}$ is convex in the positive direction if for every $z\in \Omega$, the half-line $\{z+t:t\geq 0\}$ is contained in $\Omega$. We provide necessary and sufficient conditions for the existence of an angular derivative at $\infty$ for domains convex in the positive direction which are contained either in a horizontal half-plane or in a horizontal strip. This class of domains arises naturally in the theory of semigroups of holomorphic functions, and the existence of an angular derivative has interesting consequences for the semigroup.

Article information

Source
Illinois J. Math., Volume 63, Number 3 (2019), 403-424.

Dates
Revised: 19 June 2019
First available in Project Euclid: 19 September 2019

https://projecteuclid.org/euclid.ijm/1568858865

Digital Object Identifier
doi:10.1215/00192082-7897499

Mathematical Reviews number (MathSciNet)
MR4012349

Zentralblatt MATH identifier
07110747

Citation

Karamanlis, Nikolaos. Angular derivatives and semigroups of holomorphic functions. Illinois J. Math. 63 (2019), no. 3, 403--424. doi:10.1215/00192082-7897499. https://projecteuclid.org/euclid.ijm/1568858865

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