Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 63, Number 3 (2019), 403-424.
Angular derivatives and semigroups of holomorphic functions
A simply connected domain is convex in the positive direction if for every , the half-line is contained in . 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.
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
Permanent link to this document
Digital Object Identifier
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. https://projecteuclid.org/euclid.ijm/1568858865