在希尔伯特空间中由延迟方程生成的复合协同体的谱比较
Spectral comparison of compound cocycles generated by delay equations in Hilbert spaces
AI总结：
本文提出了一种在希尔伯特空间中比较由延迟方程生成的复合协同体谱性质的方法，用于分析非线性问题中的全局稳定性。
摘要：
我们研究了在合适的希尔伯特空间中由非自治延迟方程生成的线性协同体及其扩展，称为复合协同体，到外幂。利用最近版本的频率定理，我们开发了比较此类协同体和由驻定方程生成的半群的谱性质（如均匀指数分裂）的分析技术。这些方法基于与延迟方程相关的PDEs的正则性和结构性质。特别是，所开发的工具导致了有效的稳健标准，可以保证在非线性问题中出现在全局吸引子上的闭合不变轮廓的不存在，并预计可以确保全局稳定性。
英文摘要：
We study linear cocycles generated by nonautonomous delay equations in a suitable Hilbert space and their extensions, called compound cocycles, to exterior powers. Using a recent version of the frequency theorem, we develop analytical techniques for comparing spectral properties, such as uniform exponential dichotomies, between such cocycles and semigroups generated by stationary equations. These methods are based on properties related to regularity and structure in PDEs associated with delay equations. In particular, the developed machinery leads to effective robust criteria that guarantee the absence of closed invariant contours on global attractors arising in nonlinear problems and are expected to ensure global stability.
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