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

Abstract

AbstractWe prove that a Kreiss bounded$$C_0$$C0semigroup$$(T_t)_{t \ge 0}$$(Tt)t≥0on a Hilbert space has asymptotics$$\left\| T_t\right\| = {\mathcal{O}}\big (t/\sqrt{\log (t)}\big ).$$Tt=O(t/log(t)).Then, we give an application to perturbed wave equation.