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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: 1Citation - Scopus: 1Solving an initial boundary value problem on the semiinfinite interval(Tubitak Scientific & Technological Research Council Turkey, 2016) Atalan, Ferihe; Guseinov, Gusein Sh.We explore the sign properties of eigenvalues and the basis properties of eigenvectors for a special quadratic matrix polynomial and use the results obtained to solve the corresponding linear system of differential equations on the half line subject to an initial condition at t = 0 and a condition at t = infinity.Article Citation - WoS: 27Citation - Scopus: 39Properties of the Laplace transform on time scales with arbitrary graininess(Taylor & Francis Ltd, 2011) Bohner, Martin; Guseinov, Gusein Sh.; Karpuz, BasakWe generalize several standard properties of the usual Laplace transform to the Laplace transform on arbitrary time scales. Some of these properties were justified earlier under certain restrictions on the graininess of the time scale. In this work, we have no restrictions on the graininess.Article Citation - WoS: 1ON THE DERIVATION OF EXPLICIT FORMULAE FOR SOLUTIONS OF THE WAVE EQUATION IN HYPERBOLIC SPACE(Hacettepe Univ, Fac Sci, 2013) Guseinov, Gusein Sh.We 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.Article Citation - WoS: 1Citation - Scopus: 1Spectral Method for Deriving Multivariate Poisson Summation Formulae(Amer inst Mathematical Sciences-aims, 2013) Guseinov, Gusein Sh.We show that using spectral theory of a finite family of pair-wise commuting Laplace operators and the spectral properties of the periodic Laplace operator some analogues of the classical multivariate Poisson summation formula can be derived.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 On the Resolvent of the Laplace-Beltrami Operator in Hyperbolic Space(Cambridge Univ Press, 2015) Guseinov, Gusein Sh.In this paper, a detailed description of the resolvent of the Laplace-Beltrami operator in n-dimensional hyperbolic space is given. The resolvent is an integral operator with the kernel (Green's function) being a solution of a hypergeometric differential equation. Asymptotic analysis of the solution of this equation is carried out.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: 2Existence of Solutions To Second-Order Nonlinear Discrete Elliptic Equations(Taylor & Francis Ltd, 2009) Guseinov, Gusein Sh.In this paper, we consider a boundary value problem (BVP) for second-order nonlinear partial difference equations on finite lattice domains. Some conditions are established that ensure existence and uniqueness of solutions to the BVP under consideration.
