Annals of Functional Analysis

A group structure on D and its application for composition operators

Emmanuel Fricain, Muath Karaki, and Javad Mashreghi

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Abstract

We present a group structure on D via the automorphisms which fix the point 1. Through the induced group action, each point of D 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 ψφ=λψ, where λ is a unimodular constant and φ 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 KΘ.

Article information

Source
Ann. Funct. Anal., Volume 7, Number 1 (2016), 76-95.

Dates
Received: 23 March 2015
Accepted: 23 June 2015
First available in Project Euclid: 6 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.afa/1446819350

Digital Object Identifier
doi:10.1215/20088752-3320401

Mathematical Reviews number (MathSciNet)
MR3449341

Zentralblatt MATH identifier
1343.30047

Subjects
Primary: 30D50
Secondary: 47B33: Composition operators

Keywords
composition groups Blaschke products iteration

Citation

Fricain, Emmanuel; Karaki, Muath; Mashreghi, Javad. A group structure on $\mathbb{D}$ and its application for composition operators. Ann. Funct. Anal. 7 (2016), no. 1, 76--95. doi:10.1215/20088752-3320401. https://projecteuclid.org/euclid.afa/1446819350


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