On a normal eigenvalue embedded in a continuous spectrum (Q2754835)
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scientific article; zbMATH DE number 1668455
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a normal eigenvalue embedded in a continuous spectrum |
scientific article; zbMATH DE number 1668455 |
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4 November 2001
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spectral singularity
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Friedrichs model
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Sturm-Liouville equation with delay
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perturbation
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operator of multiplication by the independent variable
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On a normal eigenvalue embedded in a continuous spectrum (English)
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It is well known that a pole of the resolvent of a closed operator on a Hilbert space generates a decomposition of the space into a root subspace and its complement. The author proves a result of this kind for a much more complicated situation of a spectral singularity embedded in the continuous spectrum of a non-selfadjoint operator. The operator in question is a special perturbation of the operator of multiplication by the independent variable. To such operators a similar problem for a Sturm-Liouville equation with delay is also reduced.
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