Bernstein functions and rates in mean ergodic theorems for operator semigroups

TL;DR

This paper develops a functional calculus framework using Bernstein functions to analyze decay rates in mean ergodic theorems for operator semigroups, also presenting new Bernstein function results.

Contribution

It introduces a novel approach employing Bernstein functions for decay rate analysis in ergodic theorems and provides new insights into Bernstein functions themselves.

Findings

Established a functional calculus method for decay rates

Linked Bernstein functions to operator semigroup analysis

Derived new properties of Bernstein functions

Abstract

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.