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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm196-3-4,
author = {Markus Haase and Yuri Tomilov},
title = {Domain characterizations of certain functions of power-bounded operators},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {265-288},
zbl = {1203.47007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm196-3-4}
}
Markus Haase; Yuri Tomilov. Domain characterizations of certain functions of power-bounded operators. Studia Mathematica, Tome 196 (2010) pp. 265-288. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm196-3-4/