A Formula for Eigenvalues of Jacobi Matrices with a Reflection Symmetry
The spectral properties of two special classes of Jacobi operators are studied. For the first class represented by the 2M-dimensional real Jacobi matrices whose entries are symmetric with respect to the secondary diagonal, a new polynomial identity relating the eigenvalues of such matrices with thei...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/9784091 |
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| Summary: | The spectral properties of two special classes of Jacobi operators are studied. For the first class represented by the 2M-dimensional real Jacobi matrices whose entries are symmetric with respect to the secondary diagonal, a new polynomial identity relating the eigenvalues of such matrices with their matrix entries is obtained. In the limit M→∞ this identity induces some requirements, which should satisfy the scattering data of the resulting infinite-dimensional Jacobi operator in the half-line, of which super- and subdiagonal matrix elements are equal to -1. We obtain such requirements in the simplest case of the discrete Schrödinger operator acting in l2(N), which does not have bound and semibound states and whose potential has a compact support. |
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| ISSN: | 1687-9120 1687-9139 |