SEMINAR:Disjointly Universal Blaschke Products and Singular Inner...

Guest:Dimitris Papathanasiou 

Title: Disjointly Universal Blaschke Products and Singular Inner Functions

Date/Time: October 14, 2024, 13:40

Location: FENS L027

Abstract: We consider two sequences of holomorphic self maps of the unit disc converging to the boundary, and the corresponding sequences of composition operators acting on the unit ball of H∞, endowed with the topology of uniform convergence on compact sets. We will characterize when such sequences of operators are disjointly universal in terms of the hyperbolic derivatives and the pseudo-hyperbolic distances of the symbols. We will also see that, whenever they exist, such disjointly universal elements can be taken to be Blaschke products. If we restrict to the non-vanishing elements of the unit ball of H∞ we will show that whenever they exist, such disjointly universal vectors can be taken to be singular inner functions. Those results provide the existence of Blaschke products and singular inner functions with certain wild boundary behaviour.