Spectral properties of non-self-adjoint perturbations for a spectral problem with involution (Q448744)
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scientific article; zbMATH DE number 6078762
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Spectral properties of non-self-adjoint perturbations for a spectral problem with involution |
scientific article; zbMATH DE number 6078762 |
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Spectral properties of non-self-adjoint perturbations for a spectral problem with involution (English)
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7 September 2012
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0.9148918
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0.90705985
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0.90307367
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0.9019635
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0.9019609
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0.90045106
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0.90037274
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0.89935136
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0.8985788
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Consider the boundary eigenvalue problem NEWLINE\[NEWLINE\begin{aligned} u'(-x)+\alpha u'(x)&=\lambda u(x),\quad -1<x< 1,\\ u(-1)&=\gamma u(1).\end{aligned}\tag{\(*\)}NEWLINE\]NEWLINE The authors prove that the eigenfunctions of \((*)\) form a Riesz basis in \(L_2(-1,1)\) provided one of the relations (a) \(\alpha^2\neq 1\), \(\gamma\neq\alpha+ \sqrt{\alpha^2-1}\), (b) \(\gamma^2\neq\pm 1\) is valid.
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