Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians
Spectral Theory
2009-02-17 v1 Classical Analysis and ODEs
Quantum Physics
Abstract
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.
Cite
@article{arxiv.0902.2464,
title = {Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians},
author = {Gusein Sh. Guseinov},
journal= {arXiv preprint arXiv:0902.2464},
year = {2009}
}