Decay of Operator Semigroups, Infinite-time Admissibility, and Related Resolvent Estimates
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866911846055804928 |
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| author | Wakaiki, Masashi |
| author_facet | Wakaiki, Masashi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_00315 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Decay of Operator Semigroups, Infinite-time Admissibility, and Related Resolvent Estimates Wakaiki, Masashi Functional Analysis Optimization and Control 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. |
| title | Decay of Operator Semigroups, Infinite-time Admissibility, and Related Resolvent Estimates |
| topic | Functional Analysis Optimization and Control |
| url | https://arxiv.org/abs/2212.00315 |