8 papers · 1 filter
Stability of Blaschke products under forward iteration
Daniela Kraus, Annika Moucha, Oliver Roth
Forward iteration of holomorphic self-maps generalizes the iteration of a single function in a natural way. This framework arises in complex dynamics, for instance in the study of…
A Schwarz-Jack lemma, circularly symmetric domains and numerical ranges
Javad Mashreghi, Annika Moucha, Ryan O'Loughlin +2
We prove a Schwarz-Jack lemma for holomorphic functions on the unit disk with the property that their maximum modulus on each circle about the origin is attained at a point on the…
A Burns-Krantz type theorem for Blaschke products
Annika Moucha
Let be a holomorphic function mapping the open unit disk into itself. We establish a boundary version of Schwarz' lemma in the spirit of a result by Burns and Krantz and provid…
Hyperbolic distortion and conformality at the boundary
Pavel Gumenyuk, Maria Kourou, Annika Moucha +1
We characterize two classical types of conformality of a holomorphic self-map of the unit disk at a boundary point - existence of a finite angular derivative in the sense of Carath…
Spectral synthesis of the invariant Laplacian and complexified spherical harmonics
Annika Moucha
We show that the space of holomorphic functions , where , possesses an orthogonal Sch…
Spectral theory of the invariant Laplacian on the disk and the sphere -- a complex analysis approach
Annika Moucha, Oliver Roth, Michael Heins
The central theme of this paper is the holomorphic spectral theory of the canonical Laplace operator of the complement $Ω:= \{(z,w) \in \widehat{\mathbb{C}}^2 \colon z \cdot w \neq…