8 results
Search Results
Now showing 1 - 8 of 8
Article Citation - WoS: 1Citation - Scopus: 1On the Eigenfunction Expansion of the Laplace-Beltrami Operator in Hyperbolic Space(Taylor & Francis Ltd, 2015) Guseinov, Gusein Sh.We describe the spectral projection of the Laplace-Beltrami operator in n-dimensional hyperbolic space by studying its resolvent as an analytic operator-valued function and applying the technique of contour integration. As a result an integral formula is established for the associated Legendre functionArticle 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: 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: 1Citation - Scopus: 1An Application of Spectral Theory of the Laplace Operator(Taylor & Francis Ltd, 2013) Guseinov, Gusein Sh.We describe the structure of arbitrary rapidly decreasing functions of the Laplace operator. Combining this with the spectral data of the periodic Laplace operator we develop a generalization of the classical Poisson summation formula.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: 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: 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.
