Geodesic
Composition of Inner Functions
Canadian journal of mathematics, Tome 66 (2014) no. 2, pp. 387-399

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DOI

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.
DOI : 10.4153/CJM-2013-002-5
Mots-clés : 30D55, 30D05, 47B33, composition operators, inner functions, Blaschke products, model subspaces 
Mashreghi, J.; Shabankhah, M. Composition of Inner Functions. Canadian journal of mathematics, Tome 66 (2014) no. 2, pp. 387-399. doi: 10.4153/CJM-2013-002-5
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     title = {Composition of {Inner} {Functions}},
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     pages = {387--399},
     year = {2014},
     volume = {66},
     number = {2},
     doi = {10.4153/CJM-2013-002-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-002-5/}
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