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

Loris Arnold

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arXiv · 2206.10426

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

Loris Arnold

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Abstract

Let $0<\alpha \leq 1$. We prove that a $\alpha$-Kreiss bounded $C_0$ semigroup $(T_t)_{t \ge 0}$ on a Hilbert space has asymptotics $||T_t|| = O\big(t^{\alpha}/\sqrt{log(t)}\big)$. Then, we give an application to perturbed wave equation.

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Loris Arnold. 2022-06-21. Behavior of Kreiss bounded $C_0$-semigroups on a Hilbert space. https://arxiv.org/abs/2206.10426

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