Domain characterizations of certainfunctions of power-bounded operators

摘要

We create a general framework for describing domains of functions ofpower-bounded operators given by power series with log-convex coefficients. This shedsnew light on recent results of Assani, Derriennic, Lin and others. In particular, we resolvean open problem regarding the "one-sided ergodic Hilbert transform" formulated in a 2001paper by Derriennic and Lin.