On the similarity of operators of the type \(\text{sgn}\,x(-\frac{d^2}{dx^2}+c\delta)\) to a normal and a selfadjoint operator. (Q1889514)
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scientific article; zbMATH DE number 2121020
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the similarity of operators of the type \(\text{sgn}\,x(-\frac{d^2}{dx^2}+c\delta)\) to a normal and a selfadjoint operator. |
scientific article; zbMATH DE number 2121020 |
Statements
On the similarity of operators of the type \(\text{sgn}\,x(-\frac{d^2}{dx^2}+c\delta)\) to a normal and a selfadjoint operator. (English)
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2 December 2004
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The authors consider the operator \(A_B = -(\text{sgn}(x))d^2/dx^2\) where the \(2\times 2\) matrix \(B\) determines the boundary conditions. They give simple necessary and sufficient conditions for the operator \(A_B\) to be similar to a normal or to a self-adjoint operator.
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spectral problem
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self-adjoint differential operator
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similarity
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quasi-Hermitian extension
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Weyl function
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