1. CJM 2013 (vol 66 pp. 387)
|Composition of Inner Functions|
We study the image of the model subspace $K_\theta$ under the composition operator $C_\varphi$, where $\varphi$ and $\theta$ are inner functions, and find the smallest model subspace which contains the linear manifold $C_\varphi K_\theta$. Then we characterize the case when $C_\varphi$ maps $K_\theta$ into itself. This case leads to the study of the inner functions $\varphi$ and $\psi$ such that the composition $\psi\circ\varphi$ is a divisor of $\psi$ in the family of inner functions.
Keywords:composition operators, inner functions, Blaschke products, model subspaces
Categories:30D55, 30D05, 47B33
2. CJM 2011 (vol 64 pp. 1329)
|Composition Operators Induced by Analytic Maps to the Polydisk|
We study properties of composition operators induced by symbols acting from the unit disk to the polydisk. This result will be involved in the investigation of weighted composition operators on the Hardy space on the unit disk and moreover be concerned with composition operators acting from the Bergman space to the Hardy space on the unit disk.
Keywords:composition operators, Hardy spaces, polydisk
Categories:47B33, 32A35, 30H10