Kato类光滑测度及其相关性质探讨

发布时间：2018-06-27 04:19

本文选题：狄氏型 + 半狄氏型　；参考：《海南师范大学》2015年硕士论文

【摘要】：E为可度量的Lusin空间,m为波莱尔σ代数,B(E)上正的σ有限测度。(ε,D(ε))为L2(E；m)上的拟正则半狄氏型,M=(Xt,Px)为(ε,D(ε))联系的m胎紧特殊标准马氏过程。对于一个(E,B(E))上的正的测度μ,如果满足μ(N)=0,其中N∈B(E)为零容集,且存在由E的紧子集组成的ε-网{Fk}k=1∞,使得对于所有的κ∈N,有μ(Fκ)∞,则我们称μ为关于(￡,D(ε))的光滑测度。记作μ∈S.在半狄氏型框架下,本文给出关于M的Kato类光滑测度的定义,得到了在一定条件下Kato类光滑测度的等价类,重点探讨了Kato类光滑测度的相关性质。第一章,我们给出本文涉及到的基本概念和记号,描述本文的背景及主要结果,并在第三节和第四节给出在对称狄氏型和非对称狄氏型框架下Kato类光滑测度已有的一些性质。第二章,在半狄氏型框架下,第二节,我们给出了Kato类光滑测度的定义,通过详细的证明,得到了热核估计下它的等价类关于Green核的光滑测度；第三节探讨了Kato类光滑测度的一系列性质,比如定理2.3.1.如果μ∈s,则存在一个由紧集组成的ε-网Fn,使得对每一个n,IEn∈SK.讲的是光滑测度s与Kato类光滑测度的关系,是对对称狄氏型框架下[3]中定理2.4的推广,本节得到的这些性质对研究半狄氏型的扰动,广义Fenman-Kac半群的强连续性、大偏差等非常重要。除了对半狄氏型框架下Kato类光滑测度的性质进行研究外,我们在第二章第四节还探讨了狄氏空间上的有界线性映射的问题。
[Abstract]:E is a measurable Lusin space, M is a finite measure of the positive Sigma on B (E). (epsilon, D (E)) is a special standard martensitic process of the quasi regular Dirichlet type on L2 (E; m). M= (Xt, Px) is a special standard Markov process associated with (epsilon)). The epsilon net {Fk}k=1 infinity consisting of a subset makes for all the kappa N (F kappa) infinity, then we call the smooth measure of (F). Under the semi dieldron framework, this paper gives the definition of the Kato class smooth measure of M, and obtains the equivalence class of the Kato class smooth measure under certain conditions, and focuses on the Kato class light. In the first chapter, we give the basic concepts and marks involved in this paper, describe the background and the main results of this article, and give some properties of the Kato class smoothness measure under symmetric dieldron and asymmetric dieldron type frames in third and fourth sections. Second, under the semi dieldron frame, second, we The definition of Kato class smooth measure is given. Through the detailed proof, the smooth measure of the equivalent class of the Green kernel is obtained under the heat kernel estimation. The third section discusses a series of properties of the Kato class smooth measure. For example, if 2.3.1., if 2.3.1., there is an epsilon net Fn which is formed by the compact set, so that every n, IEn SK. is said to be The relationship between smooth measure s and Kato class smooth measure is the extension of theorem 2.4 in [3] under symmetric Dirichlet type frame. These properties are very important for studying the perturbation of semi dieldron type, the strong continuity and large deviation of the generalized Fenman-Kac semigroup. Besides the study on the properties of the Kato class smooth measure under the semi dieldron frame, I In chapter second and fourth, we also discuss the problem of bounded linear mapping in Dirichlet space.
【学位授予单位】：海南师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O211.6

【相似文献】