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