On symmetric linear diffusions

  • 报告人: 李利平博士中科院数学与系统科学研究院
  • 报告地址: 数学学院 409报告厅
  • 报告时间: 1970-01-01
  • 主题摘要:
The main purpose of this talk is to explore the structure of local and regular Dirichlet forms associated with symmetric linear diffusions. Let (\mathcal{E}, \mathcal{F}) be a regular and local Dirichlet form on L^2(I,m), where $I$ is an interval and $m$ is a fully supported Radon measure on $I$. We shall present a complete representation for (\mathcal{E},\mathcal{F}), which shows that (\mathcal{E}, \mathcal{F}) lives on at most countable disjoint `effective' intervals with `adapted' scale function on each interval, and any point outside these intervals is a trap of the linear diffusion.  Furthermore, we shall give a necessary and sufficient condition for C_c^\infty(I) being a special standard core of  (\mathcal{E},\mathcal{F}) and identify the closure of C_c^\infty(I) in (\mathcal{E},\mathcal{F}) when C_c^\infty(I) is contained but not necessarily dense in \mathcal{F} relative to the \mathcal{E}_1-norm. This paper is partly motivated by a result of Hamza, stated in [FOT, Theorem~3.1.6] and provides a different point of view to this theorem. To illustrate our results, many examples are provided.