Classical Topics in Complex Function Theory pp 203-222 | Cite as
Automorphisms and Finite Inner Maps
Chapter
Abstract
The group Aut G and the semigroup Hol G, which were already studied in 8.4, are central to Sections 1 and 2. For bounded domains G, every sequence f n ∈ Hol G has a convergent subsequence (Montel); this fact has surprising consequences. For example, in H. Cartan’s theorem, one can read off from the convergence behavior of the sequence of iterates of a map f : G → G whether f is an automorphism of G. In 2.5, as an application of Cartan’s theorem, we give a homological characterization of automorphisms.
Keywords
Boundary Sequence Convergent Subsequence Closed Subgroup Mapping Degree Finite Blaschke Product
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