Eigenfunctions of Composition Operators on Bloch-type Spaces

Аннотация

Suppose φ is a holomorphic self map of the unit disk and C_φ is a composition operator with symbol φ that fixes the origin and 0 < |φ'(0)| < 1. This paper explores sufficient conditions that ensure all the holomorphic solutions of Schröder equation for the composition operator C_φ to belong to a Bloch-type space B_α for some α > 0. In the second part of the paper, the results obtained for composition operators are extended to the case of weighted composition operators.