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On the Structure of the Domain of a Symmetric Jump-type Dirichlet Form

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.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:28135
Date January 2012
CreatorsSchilling, René L., Uemura, Toshihiro
PublisherEMS Publishing House
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:article, info:eu-repo/semantics/article, doc-type:Text
SourcePublications of the Research Institute for Mathematical Sciences, Volume 48, Issue 1, 2012, pp. 1–20, ISSN: 1663-4926
Rightsinfo:eu-repo/semantics/openAccess
Relation10.2977/PRIMS/58

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