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Search: MSC category 30D05 ( Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX] )

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1. CJM 2013 (vol 66 pp. 387)

Mashreghi, J.; Shabankhah, M.
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

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