Orbits of non-elliptic disc automorphisms on H p

Abstract

Motivated by the Invariant Subspace Problem, we describe explicitly the closed subspace H2 generated by the limit points in the H2 norm of the orbit of a thin Blaschke product B under composition operators Cϕ induced by non-elliptic automorphisms. This description exhibits a surprising connection to model spaces. Finally, we give a constructive characterization of the Cϕ-eigenfunctions in H p for 1 p ∞.