Some remarks on Janiec uniqueness theorem for holomorphic mappings in \(\mathbb{C}^n\) (Q2769211)

Let \(B^j=\{z\in \mathbb{C}^n: \sum^\nu_{i=1} |z_\nu|^{2j} <1 \}\), \(j\in \mathbb{Z}_+\). The following theorem is proved. NEWLINENEWLINENEWLINELet \(f:B^j\to B^1\) be a holomorphic mapping of the form \(f(z)=\sum^\infty_{m=0} P^m(z)\) with \(P^m\) homogeneous polynomial mappings of degree \(m\). If \(P^j(z)= (z^j_1,\dots, z_n^j)\), then \(f=P^j\).