Final state observability in Banach spaces with applications to subordination and semigroups induced by Lévy processes

IF 1.3 4区 数学 Q1 MATHEMATICS
Dennis Gallaun, J. Meichsner, C. Seifert
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引用次数: 2

Abstract

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{\'e}vy processes.
Banach空间中的末态可观测性及其在lsamvy过程诱导的隶属和半群中的应用
将不确定性原理与耗散估计相结合,推广了证明可观测性估计的抽象方法。在这些估计中,我们允许满足可积条件的大类增长/衰减率。与以前的结果相反,我们使用迭代参数,使我们能够给出观测常数的渐近尖锐估计,并且在模型参数中是显式的。我们给出两种类型的应用,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从属半群。此外,我们将我们的结果应用于与L{\'e}vy过程相关的半群。
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来源期刊
Evolution Equations and Control Theory
Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.10
自引率
6.70%
发文量
5
期刊介绍: EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology
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