A GROUP STRUCTURE ON D AND ITS APPLICATION FOR COMPOSITION OPERATORS

作者:Fricain Emmanuel; Karaki Muath; Mashreghi Javad*
来源:Annals of Functional Analysis, 2016, 7(1): 76-95.
DOI:10.1215/20088752-3320401

摘要

We present a group structure on D via the automorphisms which fix the point 1. Through the induced group action, each point of ID 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 psi omicron psi = lambda psi, where lambda is a unimodular constant and phi 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 K-Theta

  • 出版日期2016-2

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