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Composition of Inner Functions

  Published:2013-02-13
 Printed: Apr 2014
  • J. Mashreghi,
    Département de mathématiques et de statistique, Université Laval, Québec, QC, Canada G1K 7P4
  • M. Shabankhah,
    Department of Engineering Science, College of Engineering, University of Tehran, Tehran, 11155-4563, Iran
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Abstract

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 composition operators, inner functions, Blaschke products, model subspaces
MSC Classifications: 30D55, 30D05, 47B33 show english descriptions ${H}^p$-classes
Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]
Composition operators
30D55 - ${H}^p$-classes
30D05 - Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]
47B33 - Composition operators
 

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