We characterize the structure of the domain of a pure jump-type Dirichlet form which is given by a Beurling–Deny formula. In particular, we obtain su cient conditions in terms of the jumping kernel guaranteeing that the test functions are a core for the Dirichlet form and that the form is a Silverstein extension. As an application we show that for recurrent Dirichlet forms the extended Dirichlet space can be interpreted in a natural way as a homogeneous Dirichlet space. For reflected Dirichlet spaces this leads to a simple purely analytic proof that the active reflected Dirichlet space (in the sense of Chen, Fukushima and Kuwae) coincides with the extended active reflected Dirichlet space. / Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:28135 |
| Date | January 2012 |
| Creators | Schilling, René L., Uemura, Toshihiro |
| Publisher | EMS Publishing House |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:article, info:eu-repo/semantics/article, doc-type:Text |
| Source | Publications of the Research Institute for Mathematical Sciences, Volume 48, Issue 1, 2012, pp. 1–20, ISSN: 1663-4926 |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 10.2977/PRIMS/58 |
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