Schröder Equation in Several Variables and Composition Operator

  • Cinzia Bisi

    Università degli Studi della Calabria, Arcavacata Di Rende, Italy
  • Graziano Gentili

    Università degli Studi di Firenze, Italy


Let φ\varphi be a holomorphic self-map of the open unit ball \B\B of \Cn\C^n such that φ(0)=0\varphi(0)=0 and that the differential dφ0d \varphi_{0} of φ\varphi at 00 is non singular. The study of the Schr\"oder equation in several complex variables

σφ=dφ0σ\sigma \circ \varphi = d\varphi _{0} \circ \sigma

is naturally related to the theory of composition operators on Hardy spaces of holomorphic maps on \B\B 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 φ\varphi 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. 125–134

DOI 10.4171/RLM/458