Decay of Operator Semigroups, Infinite-time Admissibility, and Related Resolvent Estimates

DOI10.1016/J.JMAA.2024.128445arXiv2212.00315MaRDI QIDQ6419190

Masashi Wakaiki

Publication date: 1 December 2022

Abstract: We study decay rates for bounded $C_0$-semigroups from the viewpoint of $L^p$-infinite-time admissibility and related resolvent estimates. In the Hilbert space setting, polynomial decay of semigroup orbits is characterized by the resolvent behavior in the open right half-plane. A similar characterization based on $L^p$-infinite-time admissibility is provided for multiplication semigroups on $L^q$-spaces with $1leqqleqp<infty$. We also give a sufficient condition for $L^2$-infinite-time admissibility for polynomially stable $C_0$-semigroups on Hilbert spaces.

Mathematics Subject Classification ID

Operator theory (47-XX) Functional analysis (46-XX)

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