arXiv subjects

Nikolaos Karamanlis

Publications and source records attributed to Nikolaos Karamanlis.

3 recordsLinked to original sources

arXiv2026

On the Bergman number of hyperbolic domains

We construct a domain $D$ in the plane whose Hardy and Bergman numbers satisfy $0<h(D)<b(D)<+\infty$. We also calculate the Bergman number for certain classes of domains having countable complement in the plane. Finally, we investigate some of the implications of our analysis in the theory of iteration of holomorphic self-maps of the unit disk. Our methods rely on estimates for the hyperbolic metric and a recent related result that connects the Bergman number with the hyperbolic metric.

math.CV↗

arXiv2023

On the monotonicity of the speeds for semigroups of holomorphic self-maps of the unit disk

We study semigroups $(ϕ_t)_{t\geq 0}$ of holomorphic self-maps of the unit disk with Denjoy-Wolff point on the boundary. We show that the orthogonal speed of such semigroups is a strictly increasing function. This answers a question raised by F. Bracci, D. Cordella, and M. Kourou, and implies a domain monotonicity property for orthogonal speeds conjectured by Bracci. We give an example of a semigroup such that its total speed is not eventually increasing. We also provide another example of a semigroup having total speed of a certain asymptotic behavior, thus answering another question of Bracci.

math.CV↗

arXiv2021

Geometric characterizations for conformal mappings in weighted Bergman spaces

We prove that a conformal mapping defined on the unit disk belongs to a weighted Bergman space if and only if certain integrals involving the harmonic measure converge. With the aid of this theorem, we give a geometric characterization of conformal mappings in Hardy or weighted Bergman spaces by studying Euclidean areas. Applying these results, we prove several consequences for such mappings that extend known results for Hardy spaces to weighted Bergman spaces. Moreover, we introduce a number which is the analogue of the Hardy number for weighted Bergman spaces. We derive various expressions for this number and hence we establish new results for the Hardy number and the relation between Hardy and weighted Bergman spaces.

math.CV↗