Spectral properties of weighted composition operators on the Bloch and Dirichlet spaces (Q2804311)

The authors study the spectra of invertible weighted composition operators on Bloch and Dirichlet spaces. These operators have the form \(f\mapsto u \cdot (f\circ\phi)\), where \(\phi\) is an automorphism of \(\mathbb D\) and \(u\) is a multiplier for these spaces which is bounded away from zero. As usual, one has to distinguish between elliptic, hyperbolic and parabolic automorphisms. There remain several open problems here.