JournalsrmiVol. 24, No. 3pp. 765–824

The linear fractional model on the ball

  • Frédéric Bayart

    Université Blaise Pascal, Aubière, France
The linear fractional model on the ball cover
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Abstract

Given a holomorphic self-map φ\varphi of the ball of CN\mathbb{C}^N, we study whether there exists a map σ\sigma and a linear fractional transformation AA such that σφ=Aσ\sigma\circ\varphi=A\circ\sigma. This is an important result when N=1N=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