Work

Complete frequencies for Koenigs domains

Year: 2025

Type: article

Abstract: We provide a complete characterization of those non-elliptic semigroups of holomorphic self-maps of the unit disc for which the linear span of eigenvectors of the generator of the corresponding semigroup of composition operators is weak-star dense in H^{\infty} . We also give some necessary and some sufficient conditions for completeness in H^{p} . This problem is equivalent to the completeness of the corresponding exponential functions in H^{\infty} (in the weak-star sense) or in H^{p} of the Koenigs domain of the semigroup. As a tool needed for the results, we introduce and study discontinuities of semigroups of holomorphic self-maps of the unit disc.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1730

Authors: Filippo Bracci, Eva A. Gallardo-Gutiérrez, Dmitry Yakubovich

Institutions: University of Rome Tor Vergata, Universidad Complutense de Madrid, Institute of Mathematical Sciences, Universidad Carlos III de Madrid, Universidad Autónoma de Madrid

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond