Abstract
We present a group structure on via the automorphisms which fix the point . Through the induced group action, each point of produces an equivalence class that turns out to be a Blaschke sequence. We show that the corresponding Blaschke products are minimal/atomic solutions of the functional equation , where is a unimodular constant and is an automorphism of the unit disk. We also characterize all Blaschke products that satisfy this equation, and we study its application in the theory of composition operators on model spaces .
Citation
Emmanuel Fricain. Muath Karaki. Javad Mashreghi. "A group structure on and its application for composition operators." Ann. Funct. Anal. 7 (1) 76 - 95, February 2016. https://doi.org/10.1215/20088752-3320401
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