# The linear fractional model on the ball

### Frédéric Bayart

Université Blaise Pascal, Aubière, France

## 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.

## Cite this article

Frédéric Bayart, The linear fractional model on the ball. Rev. Mat. Iberoam. 24 (2008), no. 3, pp. 765–824

DOI 10.4171/RMI/556