Let be a holomorphic self-map of the open unit ball of such that and that the differential of at is non singular. The study of the Schr\"oder equation in several complex variables
is naturally related to the theory of composition operators on Hardy spaces of holomorphic maps on and to the theory of discrete, complex dynamical systems. An extensive use of the infinite matrix which represents the composition operator associated to the map leads to a simpler approach, and provides new proofs, to results of existence of solutions for the Schr\"oder equation.
Cite this article
Cinzia Bisi, Graziano Gentili, Schröder Equation in Several Variables and Composition Operator. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 2, pp. 125–134DOI 10.4171/RLM/458