Dirichlet spaces and strong Markov processes
Dirichlet spaces and strong Markov processes
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狄利克雷空间和强马尔可夫过程
DOI：
10.1090/s0002-9947-1971-0295435-0
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发表时间：
1971
影响因子：
1.3
通讯作者：
M. Fukushima
中科院分区：
文献类型：
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作者：
M. Fukushima
我们证明了在每个正则狄利克雷空间的底层空间上都存在一个合适的强马尔可夫过程。然后根据相关的强马尔可夫过程描述了 A. Beurling 和 J. Deny 提出的潜在理论概念。该证明是通过发展狄利克雷空间和对称射线过程的势理论并使用基础空间的变换方法来进行的。介绍。本文是（10）的延续。我们将使用（10）中采用的那些概念和术语。令 (X, m, Y, &) 为 D 空间。如果 YA = 0，我们通过 Cap (A) = inf &'1o(u, u) 定义开集 A c X 的 (aor-) 容量，
We show that there exists a suitable strong Markov process on the underlying space of each regular Dirichlet space. Potential theoretic concepts due to A. Beurling and J. Deny are then described in terms of the associated strong Markov process. The proof is carried out by developing potential theory for Dirichlet spaces and symmetric Ray processes and by using a method of transformation of underlying spaces. Introduction. This paper is a continuation of (10). We will use those notions and terminologies adopted in (10). Let (X, m, Y, &) be a D-space. We define (aor-) capacity of an open set A c X by Cap (A) = inf &'1o(u, u) if YA = 0,