Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians

Details Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians

2009-02-14

arxiv.org/abs/0902.2464v1

SIGMA 5 (2009), 018, 28 pages

Mathematics

Spectral Theory

Scientific paper

10.3842/SIGMA.2009.018

In this paper, the concept of generalized spectral function is introduced for finite-order tridiagonal symmetric matrices (Jacobi matrices) with complex entries. The structure of the generalized spectral function is described in terms of spectral data consisting of the eigenvalues and normalizing numbers of the matrix. The inverse problems from generalized spectral function as well as from spectral data are investigated. In this way, a procedure for construction of complex tridiagonal matrices having real eigenvalues is obtained.

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