On the Relative Decay of Unbounded Semigroups on the Domain of the Generator
We study the asymptotics of $C_0$-semigroups on the domain of the generator. In particular, we analyze the behavior of $||T(t)(A-\lambda I)^{-1}||$ as time goes to infinity. Our results extend some existing results to the case when the intersection of the spectrum of the generator with the imaginary...
Збережено в:
| Дата: | 2024 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
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| Теми: | |
| Онлайн доступ: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1055 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
Репозитарії
Journal of Mathematical Physics, Analysis, Geometry| Резюме: | We study the asymptotics of $C_0$-semigroups on the domain of the generator. In particular, we analyze the behavior of $||T(t)(A-\lambda I)^{-1}||$ as time goes to infinity. Our results extend some existing results to the case when the intersection of the spectrum of the generator with the imaginary axis is non-empty. We also give a constructive example of a class of unbounded $C_0$-semigroups with pure imaginary point spectrum for which our theorem is applicable.
Mathematical Subject Classification 2020: 47D06 |
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