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Article Citation - WoS: 4Citation - Scopus: 5Construction of a Complex Jacobi Matrix From Two-Spectra(Hacettepe Univ, Fac Sci, 2011) Guseinov, Gusein Sh; MathematicsIn this paper we study the inverse spectral problem for two-spectra of finite order complex 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 deleting the first column and the first row of the Jacobi matrix. An explicit procedure of reconstruction of the matrix from the two-spectra is given.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: 1RECONSTRUCTION OF COMPLEX JACOBI MATRICES FROM SPECTRAL DATA(Hacettepe Univ, Fac Sci, 2009) Guseinov, Gusein ShIn this paper, we introduce spectral data for finite order complex Jacobi matrices and investigate the inverse problem of determining the matrix from its spectral data. Necessary and sufficient conditions for the solvability of the inverse problem are established. An explicit procedure of reconstruction of the matrix from the spectral data 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 - Scopus: 1Reconstruction of Complex Jacobi Matrices From Spectral Data(Hacettepe University, 2009) Guseinov,G.S.In this paper, we introduce spectral data for finite order complex Jacobi matrices and investigate the inverse problem of determining the matrixfrom its spectral data. Necessary and sufficient conditions for the solvability of the inverse problem are established. An explicit procedure of reconstruction of the matrix from the spectral data is given.
