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Article Citation - WoS: 1Citation - Scopus: 1An Inverse Problem for Two Spectra of Complex Finite Jacobi Matrices(Tech Science Press, 2012) Guseinov, Gusein Sh.; MathematicsThis paper deals with the inverse spectral problem for two spectra of finite order complex Jacobi matrices (tri-diagonal symmetric matrices with complex entries). The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the first diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit algorithm of reconstruction of the matrix from the two spectra is given.Article Citation - WoS: 10Citation - Scopus: 12On an Inverse Problem for Two Spectra of Finite Jacobi Matrices(Elsevier Science inc, 2012) Guseinov, Gusein Sh.We solve a version of the inverse spectral problem for two spectra of finite order real Jacobi matrices. The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the last diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit procedure of reconstruction of the matrix from the two spectra is given. (C) 2012 Elsevier Inc. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 1On Construction of a Complex Finite Jacobi Matrix From Two Spectra(int Linear Algebra Soc, 2013) Guseinov, Gusein Sh.; MathematicsThis paper concerns with the inverse spectral problem for two spectra of finite order complex Jacobi matrices (tri-diagonal symmetric matrices with complex entries). The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the last diagonal element of the Jacobi matrix by some other number. The uniqueness and existence results for solution of the inverse problem are established and an explicit procedure of reconstruction of the matrix from the two spectra is given.Article Citation - WoS: 15Citation - Scopus: 18Inverse 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.Article Citation - WoS: 3Citation - Scopus: 3An Inverse Spectral Problem for Complex Jacobi Matrices(Elsevier, 2010) Guseinov, Gusein Sh.We introduce the concept of generalized spectral function for finite order complex Jacobi matrices and solve the inverse problem with respect to the generalized spectral function. The results obtained can be used for solving of initial-boundary value problems for finite nonlinear Toda lattices with the complex-valued initial conditions by means of the inverse spectral problem method. (C) 2009 Elsevier B.V. All rights reserved.Article Citation - WoS: 5Citation - Scopus: 7Solution of the Finite Complex Toda Lattice by the Method of Inverse Spectral Problem(Elsevier Science inc, 2013) Huseynov, Aydin; Guseinov, Gusein Sh.We show that the finite Toda lattice with complex-valued initial data can be integrated by the method of inverse spectral problem. For this goal spectral data for complex Jacobi matrices are introduced and an inverse spectral problem with respect to the spectral data is solved. The time evolution of the spectral data for the Jacobi matrix associated with the solution of the Toda lattice is computed. Using the solution of the inverse spectral problem with respect to the time-dependent spectral data we reconstruct the time-dependent Jacobi matrix and hence the desired solution of the finite complex Toda lattice. (C) 2012 Elsevier Inc. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3A 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.
