On the reality of the spectrum of a non-Hermitian discrete Hamiltonian. (English) Zbl 1178.39030
The author considers a non-Hermitian second-order linear difference operator on a finite discrete interval. The focus is the reality of the spectrum. By choosing a suitable Hilbert space and defining two linear operators \(S\) and \(\Lambda\), the spectral problem is reduced to that on \(A=\Lambda^{-1}S\). This result is then applied to special cases to obtain necessary and sufficent conditions or necessary conditions for all the eigenvalues of \(A\) to be real.
Reviewer: Yuming Chen (Waterloo)
MSC:
| 39A70 | Difference operators |
| 39A12 | Discrete version of topics in analysis |
| 47A75 | Eigenvalue problems for linear operators |
| 47B39 | Linear difference operators |
References:
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