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Article Citation - WoS: 10Citation - Scopus: 12Further Properties of the Laplace Transform on Time Scales With Arbitrary Graininess(Taylor & Francis Ltd, 2013) Bohner, Martin; Guseinov, Gusein Sh; Karpuz, BasakIn this work, we generalize several properties of the usual Laplace transform to the Laplace transform on arbitrary time scales. Among them are translation theorems, transforms of periodic functions, integration of transforms, transforms of derivatives and integrals, and asymptotic values.Article Citation - WoS: 16Citation - Scopus: 19An Expansion Result for a Sturm-Liouville Eigenvalue Problem With Impulse(Tubitak Scientific & Technological Research Council Turkey, 2010) Faydaoglu, Serife; Guseinov, Gusein ShThe paper is concerned with an eigenvalue problem for second order differential equations with impulse. Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite. The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.Article Citation - WoS: 1Citation - Scopus: 1On a Quadratic Eigenvalue Problem and Its Applications(Springer Basel Ag, 2013) Atalan, Ferihe; Guseinov, Gusein ShWe investigate the eigenvalues and eigenvectors of a special quadratic matrix polynomial and use the results obtained to solve the initial value problem for the corresponding linear system of differential equations.Article Citation - WoS: 3Citation - Scopus: 3Description of the Structure of Arbitrary Functions of the Laplace-Beltrami Operator in Hyperbolic Space(Taylor & Francis Ltd, 2013) Guseinov, Gusein ShWe describe the structure of an arbitrary rapidly decreasing function of the Laplace-Beltrami operator in n-dimensional hyperbolic space showing that the function of the Laplace-Beltrami operator is an integral operator and giving an explicit formula for its kernel.Article Citation - WoS: 1Citation - Scopus: 1On Determination of a Finite Jacobi Matrix From Two Spectra(Tech Science Press, 2012) Guseinov, Gusein Sh; MathematicsIn this work we study the inverse spectral problem for two spectra of finite order real Jacobi matrices (tri-diagonal 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 first 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.
