| Acknowledgements | 第4-5页 |
| Abstract | 第5页 |
| 0 Introduction and Preliminaries | 第6-15页 |
| 0.1 Introduction | 第6-8页 |
| 0.2 Basic concepts on Dirichlet forms | 第8-12页 |
| 0.3 Linear diffusions | 第12-15页 |
| 1 Algebraic structure on Dirichlet spaces | 第15-24页 |
| 1.1 Markovian property and algebraic structure | 第16-19页 |
| 1.2 Regular representation of Dirichlet spaces and Dirichlet subspaces | 第19-22页 |
| 1.3 Dirichlet subspaces | 第22-24页 |
| 2 On regular Dirichlet subspaces of H~1(I) and associated diffusions | 第24-45页 |
| 2.1 Introduction | 第24-27页 |
| 2.2 Regular Dirichlet subspaces and scale functions | 第27-36页 |
| 2.3 Constructions by time change and state space transform | 第36-40页 |
| 2.4 Descriptions of the class S | 第40-42页 |
| 2.5 Brownian motion on finite open interval and its regular subspaces | 第42-45页 |
| 3 One dimensional local regular Dirichlet spaces and their regular subspaces | 第45-60页 |
| 3.1 Conservative local regular Dirichlet space on L~2(I,m) | 第45-50页 |
| 3.2 General local regular Dirichlet spaces on I | 第50-53页 |
| 3.3 Some properties of one dimensional local Dirichlet spaces | 第53-60页 |
| BIBLIOGRAPHY | 第60-64页 |
