Sensibility analysis of all non-zero eigenvalues of a selfadjoint compact operator (Q2718024)
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scientific article; zbMATH DE number 1606242
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sensibility analysis of all non-zero eigenvalues of a selfadjoint compact operator |
scientific article; zbMATH DE number 1606242 |
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16 January 2002
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compact selfadjoint operators depending on a parameter
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eigenvalues
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generalised directional derivatives
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generalised eigenvalues
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compact selfadjoint operator with positive eigenvalues
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selfadjoint operator with compact inverse
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0.92423946
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0.8684569
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0.8664692
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0.8633847
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0.8608552
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Sensibility analysis of all non-zero eigenvalues of a selfadjoint compact operator (English)
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Let \(A\) be a compact selfadjoint operator with positive eigenvalues on a separable Hilbert space. Let \(\lambda_m(A)\) be the \(m\)-th largest eigenvalue of \(A\). The author shows the existence of the directional derivative and the directional derivative in the sense of Clarke of \(\lambda_m(A)\) and obtains explicit formulas for these derivatives. The results are applied to study generalised eigenvalues \(Ax=\lambda Bx\), where \(A\) is compact selfadjoint and \(B\) is compact selfadjoint and positive definite, and also to study sensibility of eigenvalues of a selfadjoint operator with compact inverse.
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