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Michael’s problem and the Poincaré-Fatou-Bieberbach phenomenon. (English) Zbl 0608.32008
Let A be a Frechet algebra. The classical Michael’s problem asks whether characters on A are necessarily continuous. The authors connect this problem with well-known Bieberbach phenomenon. More precisely, if there are entire functions \(F_ n: {\mathbb{C}}^ p\to {\mathbb{C}}^ p\) such that \(\cap_{n\geq 1}(F_ 1\circ...\circ F_ n)({\mathbb{C}}^ p)=\emptyset\) then the answer to Michael’s problem would be positive. They are not able to decide whether this is true or not. But the paper contains a new method to construct functions of Bieberbach type.
Reviewer: A.Pankov

MSC:
32H25 Picard-type theorems and generalizations for several complex variables
46H05 General theory of topological algebras
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