Year: 2016
Type: preprint
Abstract: Let $\mathbb D$ be the unit disc and $z_0\in\mathbb D.$ We determine the value range $\{f(z_0)\,|\, f\in \mathcal{R}^\geq\}$, where $\mathcal{R}^\geq$ is the set of holomorphic functions $f:\mathbb D\to\mathbb D$ with $f(0)=0$ and $f'(0)\geq0$ that have only real coefficients in their power series expansion around $0$, and the smaller set $\{f(z_0)\,|\, f\in \mathcal{R}^\geq, \text{$f$ is typically real}\}.$ Furthermore, we describe a third value range $\{ f(z_0) \,|\, f \in \mathcal{I}\}$, where $\mathcal{I}$ consists of all univalent self-mappings of the upper half-plane $\mathbb{H}$ with hydrodynamical normalization which are symmetric with respect to the imaginary axis.
Source: arXiv (Cornell University)
Authors: Koch, Julia, Schleißinger, Sebastian
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2274658257