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October 2019 Angular derivatives and semigroups of holomorphic functions
Nikolaos Karamanlis
Illinois J. Math. 63(3): 403-424 (October 2019). DOI: 10.1215/00192082-7897499

Abstract

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.

Citation

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Nikolaos Karamanlis. "Angular derivatives and semigroups of holomorphic functions." Illinois J. Math. 63 (3) 403 - 424, October 2019. https://doi.org/10.1215/00192082-7897499

Information

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

zbMATH: 07110747
MathSciNet: MR4012349
Digital Object Identifier: 10.1215/00192082-7897499

Subjects:
Primary: 30D05
Secondary: 30C35, 30C45, 31A15

Rights: Copyright © 2019 University of Illinois at Urbana-Champaign

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Vol.63 • No. 3 • October 2019
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