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Article Citation - WoS: 1Citation - Scopus: 3Spectral Approach To Derive the Representation Formulae for Solutions of the Wave Equation(Hindawi Publishing Corporation, 2012) Guseinov, Gusein Sh.Using spectral properties of the Laplace operator and some structural formula for rapidly decreasing functions of the Laplace operator, we offer a novel method to derive explicit formulae for solutions to the Cauchy problem for classical wave equation in arbitrary dimensions. Among them are the well-known d'Alembert, Poisson, and Kirchhoff representation formulae in low space dimensions.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: 2Citation - Scopus: 4On a Discrete Inverse Problem for Two Spectra(Hindawi Ltd, 2012) Guseinov, Gusein Sh.A version of the inverse spectral problem for two spectra of finite-order real Jacobi matrices (tridiagonal symmetric matrices) is investigated. 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 last row and last column of the Jacobi matrix.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.
