Mean Ergodic Theorems for Bi-continuous Semigroups

TL;DR

This paper investigates the properties of Cesàro means in bi-continuous semigroups and applies these findings to Feller semigroups and evolution operators related to second-order differential operators with unbounded coefficients.

Contribution

It extends the understanding of Cesàro means in bi-continuous semigroups and provides new applications to Feller semigroups and evolution operators with unbounded coefficients.

Findings

Properties of Cesàro means for bi-continuous semigroups established

Applications to Feller semigroups with unbounded coefficients demonstrated

Results relevant for nonautonomous second-order differential operators with periodic coefficients

Abstract

In this paper we study the main properties of the Ces\`aro means of bi-continuous semigroups, introduced and studied by K\"{u}hnemund in [24]. We also give some applications to Feller semigroups generated by second-order elliptic differential operators with unbounded coefficients in $C_b(\R^N)$ and to evolution operators associated with nonautonomous second-order differential operators in $C_b(\R^N)$ with time-periodic coefficients.