Inverse spectral problems for Jacobi matrix with finite perturbed parameters (Q2822214)
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scientific article; zbMATH DE number 6630272
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inverse spectral problems for Jacobi matrix with finite perturbed parameters |
scientific article; zbMATH DE number 6630272 |
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27 September 2016
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inverse spectral problem
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Jacobi matrix
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Weyl function
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0.96303165
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0.9574074
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0.95294416
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0.95006156
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0.9468037
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0.9443222
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0.94196796
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Inverse spectral problems for Jacobi matrix with finite perturbed parameters (English)
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The author studies Jacobi matrices which have only a finite number of elements different from the corresponding elements of the canonical Jacobi matrix with 0 on the main diagonal and 1 on the secondary diagonals. For such matrices, an explicit representation of the Weyl function is obtained. As spectral data for several inverse problems, the author takes the spectral density of the absolutely continuous spectrum, with or without the eigenvalues, and the numerical parameters of the representation of one component of an eigenvector in terms of Chebyshev polynomials. Such inverse problems can have a unique solution or a finite number of solutions.
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