Orbits of non-elliptic disc automorphisms

Details Orbits of non-elliptic disc automorphisms Orbits of non-elliptic disc automorphisms

2010-02-19

arxiv.org/abs/1002.3833v2

Mathematics

Functional Analysis

18 pages, 2 figures

Scientific paper

Motivated by the Invariant Subspace Problem, we describe explicitly the closed subspace $H^2$ generated by the limit points in the $H^2$ norm of the orbit of a thin Blaschke product $B$ under composition operators $C_\phi$ induced by non-elliptic automorphisms. This description exhibits a surprising connection to model spaces. Finally, we give a constructive characterization of the $C_\phi$-eigenfunctions in $H^p$ for $1\le p\le \infty$.

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