算子半群

In Chapter 4, on the basis of introducing the theory of linear operator semigroup and the Cauchy problem in Hilbert space, this dissertation has researched the method on solving solution of distributed parameter system, and the model estimation and optimal control of the nonlinear distributed parameter system.

本文第四章在介绍线性算子半群理论及希尔伯特空间中的柯西问题的基础上，研究了分布参数系统的近似解求解方法，一类非线性分布参数系统的模型辩识和最优控制等问题。

We discuss the relevant properties of weak* continuous operator semigroups on X*.

研究X~*上弱~*连续算子半群的相关性质。

This paper also starts with this point, we introduce the concepts of weak* continuous operator semigroup and its generator on the dual of a Banach space, and discuss its relevant contents.

本文也是从这个角度出发，引入了Banach空间的对偶空间上的弱~*连续算子半群及其生成元，并对相关内容进行了讨论。

In other sections different convolution operator semigroups are discussed.

在这个基础上讨论了不同卷积算子半群的性状。

Finally, we study the eventual differentiability of a C_0-semigroup associated to a waveequation with boundary dissipation.

最后，我们讨论了一类具边界耗散的线性双曲型方程生成的算子半群的最终可微性，并利用这个结果得到了方程的解具有最终正则性以及半群满足谱决定增长条件。

The research of nonlinear ergodic theory began in the mid-seventies. Consequently, it got great development because it was widely used in many questions such as the numerical solution of differential equation, the existence theory of positive solution, control theory, optimization.

非线性算子半群的遍历理论的研究开始于二十世纪七十年代中期，随后由于被广泛应用于微分方程的数值解，正解的存在性理论，控制论，最优化等问题中而得到了很大发展。

The existence and uniqueness of the solution with the help of the Banach fixed point theorem and the theory of operator semigroups are verified .The global exponential stability of KS equation and the global exponential stability and asymptotical stability of macro KS equation with the given boundary feedbacks are proved .

通过Banach不动点原理和算子半群理论证明了方程解的存在性和唯一性，并证明了KS方程在给定的边界反馈条件下是全局指数稳定的及广义的KS方程在给定的边界反馈条件下是全局指数稳定和渐近稳定的。

This kind of problems can be described by the state-space of Co-semigroup in Hilbert space.

这样的系统可以通过Hilbert空间上的C_0算子半群作状态空间描述。

A basic problem in the studying of operator semigroup theory is the relationships between semigroups and their infinitisimal generators.

算子半群理论中研究的一个基本问题是半群与其生成元之间的关系。

The framework of the spectral theory for infinite dimensional Hamiltonian operators is construted in this project, and the relationship between semigroups of the operators and the spectral properties of the operators is found out, which is the basis of extending the separation of the variables method.

中文摘要：本项目建立了无穷维Hamilton算子的谱理论框架，揭示了其谱分布情况以及算子半群的联系，为拓宽分离变量法的应用范围提供了理论基础。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。