Behavior of Kreiss bounded $C_0$-semigroups on a Hilbert space

Abstract

Let 0 < α ≤ 1. We prove that a α-Kreiss bounded C 0 semigroup (T t ) t≥0 on a Hilbert space has asymptotics T t = O t α / log(t) . Then, we give an application to perturbed wave equation.