On stability of $N$-times integrated semigroups with nonquasianalytic growth

TL;DR

This paper investigates the long-term stability of N-times integrated semigroups with nonquasianalytic growth, extending existing theorems on the stability of bounded and C0-semigroups to a broader class.

Contribution

It extends stability results from bounded and C0-semigroups to N-times integrated semigroups with nonquasianalytic growth and invertible generators.

Findings

Extended stability theorems to N-times integrated semigroups

Generalized El Mennaoui's theorem to broader settings

Partially extended Vũ's stability results for C0-semigroups

Abstract

We discuss the behaviour at infinity of $n$-times integrated semigroups with nonquasianalytic growth and invertible generator. The results obtained extend in this setting a theorem of O. El Mennaoui on stability of bounded once integrated semigroups, and (partially) a theorem of Q. P. V$\tilde{\rm u}$ on stability of $C_0$-semigroups.