Spectra of linear fractional composition operators on the Hardy and weighted Bergman spaces of the half-plane

TL;DR

This paper computes the spectra and essential spectra of linear fractional composition operators on Hardy, weighted Bergman, and Dirichlet spaces of the upper half-plane, advancing understanding of their spectral properties.

Contribution

It extends spectral analysis of composition operators to weighted Dirichlet spaces of the upper half-plane, providing new insights into their spectral characteristics.

Findings

Computed spectra and essential spectra for these operators

Extended results to weighted Dirichlet spaces

Enhanced understanding of spectral properties in these function spaces

Abstract

We compute the spectra and the essential spectra of bounded linear fractional composition operators acting on the Hardy and weighted Bergman spaces of the upper half-plane. We are also able to extend the results to weighted Dirichlet spaces of the upper half-plane.