2017/01/10 by Liping Li, Li, Liping, Jiangang Ying +1
Chemistry · Computer Science · Mathematics · #31C25 #60J55 #60J60 #Advanced Mathematical Modeling in Engineering #Diffusion Coefficients in Liquids #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #math.PR #msc:31C25 #msc:60J55 #msc:60J60
paper · pdf · doi:10.48550/arxiv.1701.02411
openalex publication_date 2017/01/10 · arxiv created 2018/03/31 · arxiv updated 2018/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main purpose of this paper is to explore the structure of local and regular Dirichlet forms associated with symmetric linear diffusions. Let (E,F) be a regular and local Dirichlet form on L2(I,m), where I is an interval and m is a fully supported Radon measure on I. We shall first present a complete representation for (E,F), which shows that (E,F) lives on at most countable disjoint `effective' intervals with corresponding 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 Cc^∞(I) being a special standard core of (E,F) and identify the closure of Cc^∞(I) in (E,F) when Cc^∞(I) is contained but not necessarily dense in F relative to the E1-norm. This paper is partly motivated by a result of [Hamza, 1975], 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.