arXiv subjects

Eleftherios K. Theodosiadis

Publications and source records attributed to Eleftherios K. Theodosiadis.

3 recordsLinked to original sources

arXiv2026

Loewner chains with multiple boundary attraction points: A construction via close-to-convex functions

In this work we construct multi-slit \textit{chordal Loewner chains} with multiple attraction points on the real line. We build a model domain with the use of close-to-convex functions, in a way that allow us to prescribe the attraction points. These families of Loewner chains resemble the classical model for semigroups of holomorphic maps of the upper half-plane. Our work is to choose an appropriate set of arbitrarily many parameters and to study the geometric behavior of the model domain, as it evolves with respect to time, in order to derive the aforementioned Loewner chain. Finally, with the use of harmonic measure, we calculate the angles of convergence of each slit of the chain.

math.CV↗

arXiv2026

Eigenvalues for Infinitesimal Generators of Semigroups of Composition Operators

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 induced by semigroups of holomorphic functions. Depending on the type of the holomorphic semigroup and the Euclidean geometry of its Koenigs domain, we find containment relations as well as sufficient conditions for the characterization of the point spectrum of the induced infinitesimal generator. For the Dirichlet space we study all types of non-elliptic semigroups whereas for the Hardy and Bergman spaces we work on parabolic semigroups extending the work of Betsakos in the hyperbolic case.

math.CV↗

arXiv2024

Rates of convergence for holomorphic semigroups of finite shift

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 Euclidean distance, hyperbolic distance and harmonic measure. In each case, we provide explicit examples to display the sharpness of the results. We further discuss the corresponding rates of convergence for parabolic semigroups of positive hyperbolic step and infinite shift.

math.CV↗