Closability, Regularity, and Approximation by Graphs for Separable Bilinear Forms
- Authors: Hinz M.1, Teplyaev A.2
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Affiliations:
- Universität Bielefeld
- University of Connecticut
- Issue: Vol 219, No 5 (2016)
- Pages: 807-820
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/238713
- DOI: https://doi.org/10.1007/s10958-016-3149-7
- ID: 238713
Cite item
Abstract
We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic form and that normal contractions operate in a certain sense. Then we prove that a subspace of the effective domain of the quadratic form is naturally isomorphic to a core of a regular Dirichlet form on a locally compact, separable metric space. We also show that any Dirichlet form on a countably generated measure space can be approximated by essentially discrete Dirichlet forms, i.e., energy forms on finite weighted graphs, in the sense of Mosco convergence, i.e., strong resolvent convergence.
About the authors
M. Hinz
Universität Bielefeld
Author for correspondence.
Email: mhinz@math.uni-bielefeld.de
Germany, Bielefeld
A. Teplyaev
University of Connecticut
Email: mhinz@math.uni-bielefeld.de
United States, Storrs