POWER BOUNDED COMPOSITION OPERATORS IN SEVERAL VARIABLES

Abstract

Let \phi be an analytic self-map of the open unit polydisk D^N, N ∈ \mathbb{N}. Such a map induces a composition operator C_{\phi} acting on weighted Banach spaces of holomorphic functions. We study when such operators are power bounded resp. uniformly mean ergodic.

Keywords

• weighted composition operator
• weighted Banach spaces of holomorphic functions
• power bounded
• uniformly mean ergodic