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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: 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: 1Citation - Scopus: 1On Determination of a Finite Jacobi Matrix From Two Spectra(Tech Science Press, 2012) Guseinov, Gusein Sh; MathematicsIn this work we study the inverse spectral problem for two spectra of finite order real Jacobi matrices (tri-diagonal 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 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 procedure of reconstruction of the matrix from the two spectra is given.
