\(L^p\)-uniqueness of Schrödinger operators and the capacitary positive improving property (Q5937216)
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scientific article; zbMATH DE number 1618688
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^p\)-uniqueness of Schrödinger operators and the capacitary positive improving property |
scientific article; zbMATH DE number 1618688 |
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\(L^p\)-uniqueness of Schrödinger operators and the capacitary positive improving property (English)
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23 September 2002
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The author has proved several \(L^p\)-uniqueness results for Schrödinger operators by means of the Feynman-Kac formula. Using the \((m,p)\) capacity theory for Markov semigroups the author has investigated the properties of the associated Feynman-Kac semigroup. The capacity positive improving property and two new inequalities for generalized Ornstein-Uhlenbeck generators allow to show the essential self-adjointness of the ground state diffusion generator associated with two dimensional Euclidean quantum fields.
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essential self-adjointness
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Euclidean quantum fields
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\((m,p)\)-capacity
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