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Citation - WoS: 15
Citation - Scopus: 18
Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians
(Natl Acad Sci Ukraine, inst Math, 2009) Guseinov, Gusein Sh.
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.
Citation - WoS: 3
Citation - Scopus: 3
A Class of Complex Solutions To the Finite Toda Lattice
(Pergamon-elsevier Science Ltd, 2013) Guseinov, Gusein Sh.
In this paper, a class of complex-valued solutions to the finite Toda lattice is constructed by using the inverse spectral method. The corresponding Lax operator is a finite complex Jacobi matrix. As the initial values there are taken such complex numbers that the corresponding Jacobi matrix has a simple spectrum. Some examples are given. (C) 2012 Elsevier Ltd. All rights reserved.