Limiting absorption principle for singularly perturbed operators (Q2748474)
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scientific article; zbMATH DE number 1659520
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Limiting absorption principle for singularly perturbed operators |
scientific article; zbMATH DE number 1659520 |
Statements
18 March 2003
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absorption principle
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selfadjoint operator
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Dirichlet boundary conditions
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Feller semigroup
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Limiting absorption principle for singularly perturbed operators (English)
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Assume the limiting absorption principle for a selfadjoint operator \(H_1\). If \(H_2\) is another selfadjoint operator such that \((H_1- z)^{-p}- (H_2- z)^{-p}\), \(p\in\mathbb{R}\), is compact for some \(z\in \text{res }H_1\cap \text{res }H_2\), then the limiting absorption is valid also for \(H_2\). This result is applied to \(H_2\) which arise from \(H_1\) by imposing Dirichlet boundary conditions. For the unperturbed operators \(H_1\) generators of Feller semigroup are allowed.
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