Illinois Journal of Mathematics

Angular derivatives and semigroups of holomorphic functions

Nikolaos Karamanlis

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A simply connected domain ΩC is convex in the positive direction if for every zΩ, the half-line {z+t:t0} is contained in Ω. We provide necessary and sufficient conditions for the existence of an angular derivative at 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

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

Received: 17 October 2018
Revised: 19 June 2019
First available in Project Euclid: 19 September 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]
Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 30C35: General theory of conformal mappings 31A15: Potentials and capacity, harmonic measure, extremal length [See also 30C85]


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

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