Given a holomorphic self-map of the ball of , we study whether there exists a map and a linear fractional transformation such that . This is an important result when 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. 765–824DOI 10.4171/RMI/556