2 citations · 8 across the 8 of their papers we have counts for
9 papers
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…
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…
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…
A sharp Bernstein-type inequality and application to the Carleson embedding theorem with matrix weights
Daniela Kraus, Annika Moucha, Oliver Roth
We prove a sharp Bernstein-type inequality for complex polynomials which are positive and satisfy a polynomial growth condition on the positive real axis. This leads to an improved…