C-正则预解算子族的若干问题研究

发布时间：2018-02-24 10:36

本文关键词： C-正则预解算子族不变子空间容许子空间 Hille-Yosida空间不变流　出处：《扬州大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文主要研究C-正则预解算子族的相关问题,包括C-正则预解算子族的不变子空间,容许子空间,Hille-Yosida空间以及不变流等问题.全文共分为五章.第一章引言,简要介绍了 C-正则预解算子族的历史背景,以及已有的关于算子半群的不变子空间,容许子空间,Hille-Yosida空间以及不变流的结果.第二章预备知识,我们给出了 C-正则预解算子族的基本结论及性质.包括C-正则预解算子族的两个生成定理,C-正则预解算子族的指数表示定理,C-正则预解算子族的预解方程,C-正则预解算子族的一个收敛定理即λH(λ)x→ Cx.第三章,我们将C0半群的不变子空间和容许子空间推广为C-正则预解算子族的相关结论.首先我们给出了 C-正则预解算子族的不变子空间和容许子空间的概念.然后我们证明了 C-正则预解算子族不变子空间的充分必要条件.再其次我们获得了在一般Banach空间和自反Banach空间中Y是A-容许的两个刻划.最后我们得到了 C-正则预解算子族中Y是A-容许在同构意义下的刻划.第四章,我们讨论了 C-正则预解算子族的Hille-Yosida空间问题.首先我们给出了 C-正则预解算子族的Hille-Yosida空间Zk的概念,然后我们构造了一列生成元Ak,Ak在Zk中生成压缩C-正则预解算子族,并且Zk在某种意义下是最大的.最后我们获得了在a是正函数时,Ak生成压缩的C-正则半群.第五章,我们探究了非自治C-正则半群微分方程的不变流问题.首先我们给出了相切的概念,其次我们说明了不变流与切条件的等价性,最后给出了等价性的证明.
[Abstract]:In this paper, we mainly study the problems of Cregular resolvent operator family, including the invariant subspace of Cregular resolvent operator family, the admissible subspace Hille-Yosida space and the invariant flow. This paper briefly introduces the historical background of C-regular resolvent operator family, and the results of existing invariant subspaces on operator Semigroups, admissible subspaces Hille-Yosida spaces and invariant flows. In this paper, we give the basic results and properties of C- regular resolvent operator family, including two generating theorems of Cregular resolvent operator family and exponential representation theorem of C- regular resolvent operator family and C- positive solution equation of C- regular resolvent operator family. Then a convergence theorem of the family of resolvent operators is 位 H (位 X). 鈫扖hapter III, We generalize the invariant subspaces and admissible subspaces of C _ 0 Semigroups to C _ regular resolvent operator families. Firstly, we give the concepts of invariant subspaces and admissible subspaces of C-regular resolvent operators. We prove the necessary and sufficient conditions for C- regular resolvent operators to be invariant subspaces. Secondly, we obtain two characterizations that Y is A- admissible in general Banach spaces and reflexive Banach spaces. Finally, we obtain Cregular preforms. A characterization of Y in the family of solutions in the sense of A- admissible isomorphism. Chapter 4th, In this paper, we discuss the Hille-Yosida space problem of C- regular resolvent operator family. Firstly, we give the concept of Hille-Yosida space ZK of C- regular resolvent operator family, and then we construct a series of generator AK to generate compressed C- regular resolvent operator family in Zk. And ZK is the largest in some sense. Finally, we obtain a compressed C- regular semigroup generated by Ak when a is a positive function. Chapter 5th, In this paper, we investigate the invariant flow problem of nonautonomous C-regular semigroup differential equations. Firstly, we give the concept of tangent, then we show the equivalence between invariant flow and tangent conditions, and finally we prove the equivalence.
【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177

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