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Invariants of infinite Blaschke products. (English) Zbl 1164.30024

Let \(B(z)\) be an infinite Blaschke product in the unit disc \(D\) with zeros \(\{a_n\}\). The main result of the paper is the following theorem: If the Blaschke sequence \(\{a_n\}\) has a unique cluster point, then the set of continuous functions \(U: \partial D\to \partial D\) such that \(B\circ U =B\) on \(\partial D\) is an infinite cyclic group with respect to composition. The authors also consider the case where the sequence \(\{a_n\}\) has multiple cluster points forming a discrete subset of \(\partial D\), and study the analytic continuation of the invariants \(U\).

MSC:

30D50 Blaschke products, etc. (MSC2000)
30B40 Analytic continuation of functions of one complex variable
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