Bernstein functions and rates in mean ergodic theorems for operator   semigroups
  We present a functional calculus approach to the study of rates of decay in mean ergodic theorems for bounded strongly continuous operator semigroups. A central role is played by operators of the form $g(A)$, where $-A$ is the generator of the semigroup and $g$ is a Bernstein function. In addition, we obtain some new results on Bernstein functions that are of independent interest. 
Alexander Gomilko, Markus Haase, Yuri Tomilov
math.FA math.DS math.PR