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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.Conference Object Time Evolution of the Spectral Data Associated With the Finite Complex Toda Lattice(Springer-verlag Berlin, 2012) Huseynov, Aydin; Guseinov, Gusein Sh.Spectral data for complex Jacobi matrices are introduced and the time evolution of the spectral data for the Jacobi matrix associated with the solution of the finite complex Toda lattice is computed.Article Citation - WoS: 47Citation - Scopus: 63The Convolution on Time Scales(Hindawi Publishing Corporation, 2007) Bohner, Martin; Guseinov, Gusein Sh.The main theme in this paper is an initial value problem containing a dynamic version of the transport equation. Via this problem, the delay (or shift) of a function defined on a time scale is introduced, and the delay in turn is used to introduce the convolution of two functions defined on the time scale. In this paper, we give some elementary properties of the delay and of the convolution and we also prove the convolution theorem. Our investigation contains a study of the initial value problem under consideration as well as some results about power series on time scales. As an extensive example, we consider the q-difference equations case. Copyright (c) 2007 M. Bohner and G. Sh. Guseinov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.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: 15Multiple Lebesgue Integration on Time Scales(Hindawi Publishing Corporation, 2006) Bohner, Martin; Guseinov, Gusein Sh.We study the process of multiple Lebesgue integration on time scales. The relationship of the Riemann and the Lebesgue multiple integrals is investigated. Copyright (c) 2006 M. Bohner and G. Sh. Guseinov.
