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arXiv · 2212.00315

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

Masashi Wakaiki
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Abstract

We study decay rates for bounded $C_0$-semigroups from the perspective 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 $1 \leq q \leq p < \infty$. For polynomially stable $C_0$-semigroups on Hilbert spaces, we also give a sufficient condition for $L^2$-infinite-time admissibility.

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Masashi Wakaiki. 2022-12-01. Decay of Operator Semigroups, Infinite-time Admissibility, and Related Resolvent Estimates. https://arxiv.org/abs/2212.00315

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