14 citations · 44 across the 24 of their papers we have counts for
33 papers
The strong form of the Ahlfors-Schwarz lemma at the boundary and a rigidity result for Liouville's equation
Filippo Bracci, Daniela Kraus, Oliver Roth
We prove a boundary version of the strong form of the Ahlfors-Schwarz lemma with optimal error term. This result provides nonlinear extensions of the boundary Schwarz lemma of Burn…
Function Theory off the complexified unit circle: Fréchet space structure and automorphisms
Michael Heins, Annika Moucha, Oliver Roth
Motivated by recent work on strict deformation quantization of the unit disk and the Riemann sphere, we study the Fréchet space structure of the set of holomorphic functions on the…
Strict Wick-type deformation quantization on Riemann surfaces: Rigidity and Obstructions
Daniela Kraus, Oliver Roth, Sebastian Schleissinger +1
Let be a hyperbolic Riemann surface. We study a convergent Wick-type star product on which is induced by the canonical convergent star product $\star_{\mathbb{D}}…
Peschl-Minda derivatives and convergent Wick star products on the disk, the sphere and beyond
Michael Heins, Annika Moucha, Oliver Roth +1
We introduce and study invariant differential operators acting on the space of holomorphic functions on the complement ${Ω=\{(z,w) \in \hat{\mathbb{C}}^2 \, : \, z…
The angular derivative problem for petals of one-parameter semigroups in the unit disk
Pavel Gumenyuk, Maria Kourou, Oliver Roth
We study the angular derivative problem for petals of one-parameter semigroups of holomorphic self-maps of the unit disk. For hyperbolic petals we prove a necessary and sufficient…
The Nehari-Schwarz lemma and infinitesimal boundary rigidity of bounded holomorphic functions
Oliver Roth
We survey a number of recent generalizations and sharpenings of Nehari's extension of Schwarz' lemma for holomorphic self-maps of the unit disk. In particular, we discuss the case…