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This article is cited in 1 scientific paper (total in 1 paper)
Mathematics
Probabilistic characterizations of essential self-adjointness and removability of singularities
M. Hinza, S.-J. Kangb, J. Masamunec a University of Bielefeld
b Seoul National University
c Hokkaido University
Abstract:
We consider the Laplacian and its fractional powers of order less than one on the complement $\mathbb{R}^d\setminus\Sigma$ of a given compact set $\Sigma\subset \mathbb{R}^d$ of zero Lebesgue measure. Depending on the size of $\Sigma$, the operator under consideration, equipped with the smooth compactly supported functions on $\mathbb{R}^d \setminus \Sigma$, may or may not be essentially self-ajoint. We survey well-known descriptions for the critical size of $\Sigma$ in terms of capacities and Hausdorff measures. In addition, we collect some known results for certain two-parameter stochastic processes. What we finally want to point out is, that, although a priori essential self-adjointness is not a notion directly related to classical probability, it admits a characterization via Kakutani-type theorems for such processes.
Keywords:
Laplacian, essential self-adjointness, removability of singularities, probabilistic characterizations, stochastic processes.
Citation:
M. Hinz, S.-J. Kang, J. Masamune, “Probabilistic characterizations of essential self-adjointness and removability of singularities”, Mathematical Physics and Computer Simulation, 20:3 (2017), 148–162
Linking options:
https://www.mathnet.ru/eng/vvgum189 https://www.mathnet.ru/eng/vvgum/v20/i3/p148
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Abstract page: | 617 | Full-text PDF : | 49 | References: | 29 |
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