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Composition of Inner Functions

Published online by Cambridge University Press:  20 November 2018

J. Mashreghi  and
M. Shabankhah
J. Mashreghi
Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec, QC, Canada G1K 7P4.. e-mail: javad.mashreghi@mat.ulaval.ca
M. Shabankhah
Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec, QC, Canada G1K 7P4.. e-mail: javad.mashreghi@mat.ulaval.ca
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Abstract

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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 \,\text{o}\,\varphi $ is a divisor of $\psi $ in the family of inner functions.

Keywords

30D5530D0547B33composition operatorsinner functionsBlaschke productsmodel subspaces
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 66 , Issue 2 , 01 April 2014 , pp. 387 - 399
Copyright
Copyright © Canadian Mathematical Society 2014

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