Composition Operators and Schröder’s Functional Equation
نویسندگان
چکیده
In Schröder’s equation, φ is the given quantity, a holomorphic selfmap of the unit disc U = {z ∈ C : |z| < 1}, and the goal is to find λ ∈ C and f holomorphic on U so that (1) is satisfied. Schröder’s equation is, of course, the eigenvalue equation for the composition operator Cφ, defined by Cφf = f ◦φ, where, at least for now, f is allowed to range through the entire space H(U) of functions holomorphic on U . The study I want to describe begins with a question that has long intrigued me:
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