arXiv subjects

Davide Cordella

Publications and source records attributed to Davide Cordella.

4 recordsLinked to original sources

arXiv2023

Multipoint Schwarz-Pick Lemma for the quaternionic case

Following ideas by Beardon, Minda and Baribeau, Rivard, Wegert in the context of the complex Schwarz-Pick Lemma, we use iterated hyperbolic difference quotients to prove a quaternionic multipoint Schwarz-Pick Lemma, in the context of the theory of slice regular functions. As applications, we obtain quaternionic Dieudonn\'e and Goluzin estimates. Finally, an algorithm for the construction of (Nevanlinna-Pick) interpolating slice regular functions with real nodes is provided as a byproduct of the quaternionic multipoint Schwarz-Pick Lemma.

math.CV↗

arXiv2022

Holomorphic semigroups of finite shift in the unit disc

We give three necessary and sufficient conditions so that a parabolic holomorphic semigroup $(ϕ_t)$ in the unit disc is of finite shift. One is in terms of the asymptotic behavior of speeds of convergence, the second one is related to the hyperbolic metric of its Koenigs domain $Ω$ and the latter one deals with Euclidean properties of $Ω$.

math.CV↗

arXiv2021

Asymptotic upper bound for tangential speed of parabolic semigroups of holomorphic self-maps in the unit disc

We show that the tangential speed of a parabolic semigroup of holomorphic self-maps in the unit disc is asymptotically bounded from above by (1/2)logt, proving a conjecture by Bracci. In order to show the proof we need a result of "asymptotical monotonicity" of the tangential speed for proper pairs of parabolic semigroups with positive hyperbolic step.

math.CV↗

arXiv2021

Asymptotic monotonicity of the orthogonal speed and rate of convergence for semigroups of holomorphic self-maps of the unit disc

We show that the orthogonal speed of semigroups of holomorphic self-maps of the unit disc is asymptotically monotone in most cases. Such a theorem allows to generalize previous results of D. Betsakos and D. Betsakos, M. D. Contreras and S. Díaz-Madrigal and to obtain new estimates for the rate of convergence of orbits of semigroups.

math.CV↗