2016/02/16 by Julia Koch, Koch, Julia, Sebastian Schleißinger +1
Mathematics · #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Analytic and geometric function theory
paper · pdf · doi:10.48550/arxiv.1602.05058
Let \mathbb D be the unit disc and z0∈\mathbb D. We determine the value range \f(z0) | f∈ R^≥\, where R^≥ is the set of holomorphic functions f:\mathbb D→\mathbb D with f(0)=0 and f'(0)≥0 that have only real coefficients in their power series expansion around 0, and the smaller set \f(z0) | f∈ R^≥, f is typically real\. Furthermore, we describe a third value range \ f(z0) | f ∈ I\, where I consists of all univalent self-mappings of the upper half-plane ℍ with hydrodynamical normalization which are symmetric with respect to the imaginary axis.