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Order of linearly invariant family of mappings in \({\mathbb{C}}^n\). (English) Zbl 1026.32032

Summary: We suggest a new definition of the order of a linearly invariant family of locally biholomorphic mappings of the unit ball in \(\mathbb{C}^n\). This definition is equivalent to the one given by Pfaltzgraff in [J. A. Pfaltzgraff, Complex Variables, Theory Appl. 33, 239-253 (1997; Zbl 0912.32017)]. It bases on a very simple relationship with the Jacobian of the mapping (see Corollary 1). It appears that the order of a mapping depends only on its Jacobian (see Proposition 1).

MSC:

32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables

Citations:

Zbl 0912.32017
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