Polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in \(\mathbb{R}^ n, n\geq{}3\), odd (Q1191045)
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scientific article; zbMATH DE number 59010
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in \(\mathbb{R}^ n, n\geq{}3\), odd |
scientific article; zbMATH DE number 59010 |
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Polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in \(\mathbb{R}^ n, n\geq{}3\), odd (English)
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27 September 1992
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The author obtains an upper bound for the number of scattering poles of compactly supported metric perturbations of the Laplacian in \(\mathbb{R}^ n\). More precisely, one gets that the number of such poles inside the ball of radius \(r\) is bounded by a constant times \(r^{n+1}\) as \(r\) tends to infinity. For this purpose, the author proves sharp estimates on the cut-off resolvent of the free Laplacian and uses the Phragmen- Lindelöf principle.
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cut-off resolvent of the free Laplacian
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Phragmen-Lindelöf principle
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