Abstract
A subset \(\Omega \subseteq \mathbb{C}{^n}\) will be called a domain if it is connected and open. The automorphism group Aut \((\Omega)\) of \(\Omega\) is by definition the set of all holomorphic mappings \(f:\Omega \to \Omega\) with inverse map \({f^{ - 1}}\) existing and also holomorphic. The group operation is the composition of mappings, and it is easy to check that this binary operation makes Aut \((\Omega)\) into a group.
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© 2011 Springer Science+Business Media, LLC
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Greene, R.E., Kim, KT., Krantz, S.G. (2011). Preliminaries. In: The Geometry of Complex Domains. Progress in Mathematics, vol 291. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4622-6_1
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DOI: https://doi.org/10.1007/978-0-8176-4622-6_1
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Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4139-9
Online ISBN: 978-0-8176-4622-6
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