2014
DOI: 10.1002/mana.201300322
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A remark on the uniqueness of Silverstein extensions of symmetric Dirichlet forms

Abstract: We prove the uniqueness of the Silverstein extension of symmetric Dirichlet forms under some condition on intrinsic metrics. As its application, we present some non‐local Dirichlet forms which possess the uniqueness of the Silverstein extension and generate non‐conservative Hunt processes.

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Cited by 9 publications
(7 citation statements)
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“…For strongly local regular Dirichlet forms, the uniqueness of Silverstein extensions was proven by Kawabata and Takeda [30] in the case when the underlying space is metrically complete with respect to the Carnot-Caratheodori distance. This result was extended to general regular Dirichlet forms by Kuwae and Shiozawa [34] using the intrinsic distance defined by Frank, Lenz, and Wingert in [11].…”
Section: Introductionmentioning
confidence: 89%
“…For strongly local regular Dirichlet forms, the uniqueness of Silverstein extensions was proven by Kawabata and Takeda [30] in the case when the underlying space is metrically complete with respect to the Carnot-Caratheodori distance. This result was extended to general regular Dirichlet forms by Kuwae and Shiozawa [34] using the intrinsic distance defined by Frank, Lenz, and Wingert in [11].…”
Section: Introductionmentioning
confidence: 89%
“…(ii) Even though the process is not conservative, we have the following information from the adapted metric: if any ball associated with the adapted metric is relatively compact, then the Silverstein extension of the corresponding Dirichlet form is uniquely determined (see [21]). Roughly speaking, this means that we can not extend the process after the lifetime.…”
Section: Examplesmentioning
confidence: 99%
“…Our second question on uniqueness of self-adjoint restrictions of discrete Laplacians and discrete magnetic Schrödinger operators has seen quite some attention in recent years, see [5,6,7,11,12,13,14,18,21,23,24,27,28,33,38,40,41,42,43,53,54,56,57] among others.…”
Section: Introductionmentioning
confidence: 99%