Browsing by Author "Guseinov, Gusein Sh."
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Article Citation Count: 1An application of spectral theory of the Laplace operator(Taylor & Francis Ltd, 2013) Hüseyin, Hüseyin Şirin; MathematicsWe 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 Count: 11Boundary value problems for nonlinear impulsive Hamiltonian systems(Elsevier Science Bv, 2014) Hüseyin, Hüseyin Şirin; MathematicsWe study two point boundary value problems for nonlinear impulsive Hamiltonian systems. Spectral analysis of the corresponding linear impulsive Hamiltonian system and a fixed point theorem are employed to obtain an existence and uniqueness result for solutions of the nonlinear problem. Two examples are given in which the main condition is made explicit. (C) 2013 Elsevier B.V. All rights reserved.Article Citation Count: 4A class of complex solutions to the finite Toda lattice(Pergamon-elsevier Science Ltd, 2013) Hüseyin, Hüseyin Şirin; MathematicsIn 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.Article Citation Count: 45The convolution on time scales(Hindawi Publishing Corporation, 2007) Hüseyin, Hüseyin Şirin; Guseinov, Gusein Sh.; MathematicsThe 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 Count: 82Double integral calculus of variations on time scales(Pergamon-elsevier Science Ltd, 2007) Hüseyin, Hüseyin Şirin; Guseinov, Gusein Sh.; MathematicsWe consider a version of the double integral calculus of variations on time scales, which includes as special cases the classical two-variable calculus of variations and the discrete two-variable calculus of variations. Necessary and sufficient conditions for a local extremum are established, among them an analogue of the Euler-Lagrange equation. (C) 2007 Elsevier Ltd. All rights reserved.Article Citation Count: 2Existence of solutions to second-order nonlinear discrete elliptic equations(Taylor & Francis Ltd, 2009) Hüseyin, Hüseyin Şirin; MathematicsIn 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.Article Citation Count: 33Higher-order self-adjoint boundary-value problems on time scales(Elsevier Science Bv, 2006) Hüseyin, Hüseyin Şirin; Guseinov, Gusein Sh.; Hoffacker, Joan; MathematicsIn this study, higher-order self-adjoint differential expressions on time scales and their associated self-adjoint boundary conditions are discussed. The symmetry property of the corresponding Green's functions is shown, together with specific formulas of Green's functions for select time scales. (c) 2005 Elsevier B.V. All rights reserved.Article Citation Count: 53The h-Laplace and q-Laplace transforms(Academic Press inc Elsevier Science, 2010) Hüseyin, Hüseyin Şirin; Guseinov, Gusein Sh.; MathematicsStarting with a general definition of the Laplace transform on arbitrary time scales, we specify the particular concepts of the h-Laplace and q-Laplace transforms. The convolution and inversion problems for these transforms are considered in some detail. (c) 2009 Elsevier Inc. All rights reserved.Article Citation Count: 3An inverse spectral problem for complex Jacobi matrices(Elsevier, 2010) Hüseyin, Hüseyin Şirin; MathematicsWe introduce the concept of generalized spectral function for finite order complex Jacobi matrices and solve the inverse problem with respect to the generalized spectral function. The results obtained can be used for solving of initial-boundary value problems for finite nonlinear Toda lattices with the complex-valued initial conditions by means of the inverse spectral problem method. (C) 2009 Elsevier B.V. All rights reserved.Article Citation Count: 3Inverse spectral problem for finite Jacobi matrices with zero diagonal(Taylor & Francis Ltd, 2015) Aydın, Ayhan; Guseinov, Gusein Sh.; Hüseyin, Hüseyin Şirin; MathematicsIn this study, the necessary and sufficient conditions for solvability of an inverse spectral problem about eigenvalues and normalizing numbers for finite-order real Jacobi matrices with zero diagonal elements are established. Anexplicit procedure of reconstruction of the matrix from the spectral data consisting of the eigenvalues and normalizing numbers is given. Numerical examples and error analysis are provided to demonstrate the solution technique of the inverse problem. The results obtained are used to justify the solving procedure of the finite Langmuir lattice by the method of inverse spectral problem.Article Citation Count: 14Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians(Natl Acad Sci Ukraine, inst Math, 2009) Hüseyin, Hüseyin Şirin; MathematicsIn 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 Count: 10The Laplace transform on isolated time scales(Pergamon-elsevier Science Ltd, 2010) Hüseyin, Hüseyin Şirin; Guseinov, Gusein Sh.; MathematicsStarting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse Laplace transform. The concept of convolution is considered in more detail by proving the convolution theorem and a discrete analogue of the classical theorem of Titchmarsh for the usual continuous convolution. (C) 2010 Elsevier Ltd. All rights reserved.Article Citation Count: 17Line integrals and Green's formula on time scales(Academic Press inc Elsevier Science, 2007) Hüseyin, Hüseyin Şirin; Guseinov, Gusein Sh.; MathematicsIn this paper we study curves parametrized by a time scale parameter, introduce line delta and nabla integrals along time scale curves, and obtain an analog of Green's formula in the time scale setting. (c) 2006 Elsevier Inc. All rights reserved.Article Citation Count: 9Multiple Lebesgue integration on time scales(Hindawi Publishing Corporation, 2006) Hüseyin, Hüseyin Şirin; Guseinov, Gusein Sh.; MathematicsWe 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.Article Citation Count: 2On a Discrete Inverse Problem for Two Spectra(Hindawi Ltd, 2012) Hüseyin, Hüseyin Şirin; MathematicsA 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 Count: 8On an inverse problem for two spectra of finite Jacobi matrices(Elsevier Science inc, 2012) Hüseyin, Hüseyin Şirin; MathematicsWe solve a version of the inverse spectral problem for two spectra of finite order real Jacobi matrices. 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 another 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. (C) 2012 Elsevier Inc. All rights reserved.Article Citation Count: 1On the eigenfunction expansion of the Laplace-Beltrami operator in hyperbolic space(Taylor & Francis Ltd, 2015) Hüseyin, Hüseyin Şirin; MathematicsWe 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 Count: 7On the impulsive boundary value problems for nonlinear Hamiltonian systems(Wiley, 2016) Hüseyin, Hüseyin Şirin; MathematicsIn this work, we deal with two-point boundary value problems for nonlinear impulsive Hamiltonian systems with sub-linear or linear growth. A theorem based on the Schauder fixed point theorem is established, which gives a result that yields existence of solutions without implications that solutions must be unique. An upper bound for the solution is also established. Examples are given to illustrate the main result. Copyright (C) 2016 John Wiley & Sons, Ltd.Article Citation Count: 0ON THE RESOLVENT OF THE LAPLACE-BELTRAMI OPERATOR IN HYPERBOLIC SPACE(Cambridge Univ Press, 2015) Hüseyin, Hüseyin Şirin; MathematicsIn 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 Count: 24Properties of the Laplace transform on time scales with arbitrary graininess(Taylor & Francis Ltd, 2011) Hüseyin, Hüseyin Şirin; Guseinov, Gusein Sh.; Karpuz, Basak; MathematicsWe 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.