Weighted Composition Operators: Isometries and Asymptotic Behaviour

This paper studies the behaviour of iterates of weigh\-ted composition operators acting on spaces of analytic functions, with particular emphasis on the Hardy space H². Questions relating to uniform, strong and weak convergence are resolved in many cases. Connected to this is the question when a weighted composition operator is an isometry, and new results are given in the case of the Hardy and Bergman spaces.