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Automorphisms and Finite Inner Maps

  • Reinhold Remmert
Part of the Graduate Texts in Mathematics book series (GTM, volume 172)

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Reinhold Remmert
    • 1
  1. 1.Mathematisches InstitutWestfälische Wilhelms—Universität MünsterMünsterGermany

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