The linear fractional model on the ball
Frédéric
Bayart
Source: Rev. Mat. Iberoamericana Volume 24, Number 3
(2008), 765-824.
Abstract
Given a holomorphic self-map $\varphi$ of the ball of $\mathbb{C}^N$, we study whether there exists a map $\sigma$ and a linear fractional transformation $A$ such that $\sigma\circ\varphi=A\circ\sigma$. This is an important result when $N=1$ with a great number of applications. We extend this result to the multi-dimensional setting for a large class of maps. Applications to commuting holomorphic self-maps are given.
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Permanent link to this document: http://projecteuclid.org/euclid.rmi/1228834294
Zentralblatt MATH identifier: 05509263
Mathematical Reviews number (MathSciNet): MR2490162
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