Browsing by Author "Guseinov,G.S."
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Conference Object Inverse Spectral Problems for Complex Jacobi Matrices(Springer New York LLC, 2013) Guseinov,G.S.; MathematicsThe paper deals with two versions of the inverse spectral problem for finite complex Jacobi matrices. The first is to reconstruct the matrix using the eigenvalues and normalizing numbers (spectral data) of the matrix. The second is to reconstruct the matrix using two sets of eigenvalues (two spectra), one for the original Jacobi matrix and one for the matrix obtained by deleting the last row and last column of the Jacobi matrix. Uuniqueness and existence results for solution of the inverse problems are established and an explicit procedure of reconstruction of the matrix from the spectral data is given. It is shown how the results can be used to solve finite Toda lattices subject to the complex-valued initial conditions. © Springer Science+Business Media New York 2013.Article Citation - Scopus: 1On the Derivation of Explicit Formulae for Solutions of the Wave Equation in Hyperbolic Space(Hacettepe University, 2013) Guseinov,G.S.; MathematicsWe offer a new approach to solving the initial value problem for the wave equation in hyperbolic space in arbitrary dimensions. Our approach is based on the spectral analysis of the Laplace-Beltrami operator in hyperbolic space and some structural formulae for rapidly decreasing functions of this operator. © 2013, Hacettepe University. All rights reserved.Article Citation - Scopus: 1Reconstruction of Complex Jacobi Matrices From Spectral Data(Hacettepe University, 2009) Guseinov,G.S.; MathematicsIn 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.
