论文标题
Banach空间中的最终状态可观察性，其适用于下属和由L {é} Vy过程引起的半群
Final State Observability in Banach spaces with applications to Subordination and Semigroups induced by L{é}vy processes
论文作者
论文摘要
本文通过结合不确定性原理和耗散估计来证明可观察性估计的抽象方法。在这些估计中，我们允许大量的增长/衰减速率满足整合性条件。与以前的结果相反，我们使用了一个迭代参数，使我们能够对观察常数进行渐近的清晰估计，并且在模型参数中是显式的。我们提供两种类型的应用，其中自然出现增长/衰减率的扩展。通过利用从属技术，我们展示了半群的耗散估计如何转移到下属的半群中。此外，我们将结果应用于与L {é} Vy过程有关的半群。
This paper generalizes the abstract method of proving an observability estimate by combining an uncertainty principle and a dissipation estimate. In these estimates we allow for a large class of growth/decay rates satisfying an integrability condition. In contrast to previous results, we use an iterative argument which enables us to give an asymptotically sharp estimate for the observation constant and which is explicit in the model parameters. We give two types of applications where the extension of the growth/decay rates naturally appear. By exploiting subordination techniques we show how the dissipation estimate of a semigroup transfers to subordinated semigroups. Furthermore, we apply our results to semigroups related to L{é}vy processes.
