Probabilistic characterizations of essential self-adjointness and removability of singularities

Автор: Hinz Michael, Kang Seunghyun, Masamune Jun

Журнал: Математическая физика и компьютерное моделирование @mpcm-jvolsu

Рубрика: Математика

Статья в выпуске: 3 (40), 2017 года.

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We consider the Laplacian and its fractional powers of order less than one on the complement R� \ Σ of a given compact set Σ C R� of zero Lebesgue measure. Depending on the size of Σ, the operator under consideration, equipped with the smooth compactly supported functions on R� \ Σ, may or may not be essentially self-ajoint. We survey well-known descriptions for the critical size of Σ 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.

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Laplacian, essential self-adjointness, removability of singularities, probabilistic characterizations, stochastic processes

Короткий адрес: https://sciup.org/14968903

IDR: 14968903   |   DOI: 10.15688/mpcm.jvolsu.2017.3.11

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