The α-orthogonal complements of regular Dirichlet subspaces for one-dimensional Brownian motion

详细信息    查看全文

• 作者：LiPing Li ; XiuCui Song
• 关键词：Dirichlet form ; regular Dirichlet subspace ; harmonic equation ; Neumann type condition
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：59
• 期：10
• 页码：2019-2026
• 全文大小：162 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862
• 卷排序：59

文摘

Roughly speaking a regular Dirichlet subspace of a Dirichlet form is a subspace which is also a regular Dirichlet form on the same state space. In particular, the domain of regular Dirichlet subspace is a closed subspace of the Hilbert space induced by the domain and α-inner product of original Dirichlet form. We investigate the orthogonal complement of regular Dirichlet subspace for one-dimensional Brownian motion in this paper. Our main results indicate that this orthogonal complement has a very close connection with the α-harmonic equation under Neumann type condition.