3 citations · 4 across the 11 of their papers we have counts for
13 papers
Riesz -capacity of Cantor sets and cyclicity in Dirichlet-type spaces
Dimitrios Vavitsas, Jujie Wu, Konstantinos Zarvalis
We examine the threshold of the cyclicity for functions in Dirichlet-type spaces , . Given a fixed , we construct a holomorphic function $f…
Semigroup models for discrete holomorphic iteration in the unit disc
Argyrios Christodoulou, Konstantinos Zarvalis
The main goal of this article is to develop a technique that allows us to partially embed the orbit of any holomorphic self-map of the disc, into a semigroup which captures the…
Extremal rate of convergence in continuous dynamics
Francisco J. Cruz-Zamorano, Konstantinos Zarvalis
This paper deals with semigroups of holomorphic self-maps of the upper half-plane that exhibit an extremal (i.e. the slowest possible) rate of convergence to their Denjoy--Wolff po…
Extremal rate of convergence in discrete hyperbolic and parabolic dynamics
Francisco J. Cruz-Zamorano, Konstantinos Zarvalis
This paper investigates the dynamical behaviour of holomorphic self-maps of the upper half-plane. More precisely, we focus on the hyperbolic and parabolic self-maps whose orbits ap…
Eigenvalues for Infinitesimal Generators of Semigroups of Composition Operators
Maria Kourou, Eleftherios K. Theodosiadis, Konstantinos Zarvalis
We study the eigenvalues for infinitesimal generators of semigroups of composition operators acting on Hardy spaces, Bergman spaces, and the Dirichlet space. Such semigroups are in…
Monotonicity properties of hyperbolic projections in holomorphic iteration
Argyrios Christodoulou, Konstantinos Zarvalis
We consider hyperbolic projections of orbits of holomorphic self-maps of the unit disc, onto curves landing on the unit circle with a given angle. We show that under certain, neces…
On the rates of convergence of orbits in semigroups of holomorphic functions
Dimitrios Betsakos, Francisco J. Cruz-Zamorano, Konstantinos Zarvalis
Let be a continuous semigroup of holomorphic self-maps of the unit disk with Denjoy-Wolff point . We study the rate of convergence o…
Semigroups of holomorphic functions; rectifiability and Lipschitz properties of the orbits
Dimitrios Betsakos, Konstantinos Zarvalis
Let be a semigroup of holomorphic functions in the unit disk. We prove that all its orbits are rectifiable and that its forward orbits are Lipschitz curves. Moreover, we fi…
Rates of convergence for holomorphic semigroups of finite shift
Maria Kourou, Eleftherios K. Theodosiadis, Konstantinos Zarvalis
We study parabolic semigroups of finite shift in the unit disk with regard to the rate of convergence of their orbits to the Denjoy--Wolff point. We examine this rate in terms of E…
Geometric description of some Loewner chains with infinitely many slits
Eleftherios Theodosiadis, Konstantinos Zarvalis
We study the chordal Loewner equation associated with certain driving functions that produce infinitely many slits. Specifically, for a choice of a sequence of positive numbers $(b…
Speeds of Convergence for Petals of Semigroups of Holomorphic Functions
Maria Kourou, Konstantinos Zarvalis
We study the backward dynamics of one-parameter semigroups of holomorphic self-maps of the unit disk. More specifically, we introduce the speeds of convergence for petals of the se…
Quasi-geodesics and backward orbits under semigroups of holomorphic functions
Konstantinos Zarvalis
We explore two properties of backward orbits under semigroups of holomorphic self-maps in the unit disk. First, we prove that regular backward orbits are quasi-geodesics for the hy…
Compact Sets in Petals and their Backward Orbits under Semigroups of Holomorphic Functions
Maria Kourou, Konstantinos Zarvalis
Let be a semigroup of holomorphic functions in the unit disk and a compact subset of . We investigate the conditions under which the…