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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: 4Citation - Scopus: 5Construction of a Complex Jacobi Matrix From Two-Spectra(Hacettepe Univ, Fac Sci, 2011) Guseinov, Gusein Sh; MathematicsIn this paper we study the inverse spectral problem for two-spectra of finite order complex 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 deleting the first column and the first row of the Jacobi matrix. An explicit procedure of reconstruction of the matrix from the two-spectra is given.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: 1RECONSTRUCTION OF COMPLEX JACOBI MATRICES FROM SPECTRAL DATA(Hacettepe Univ, Fac Sci, 2009) Guseinov, Gusein ShIn this paper, we introduce spectral data for finite order complex Jacobi matrices and investigate the inverse problem of determining the matrix from its spectral data. Necessary and sufficient conditions for the solvability of the inverse problem are established. An explicit procedure of reconstruction of the matrix from the spectral data is given.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: 64Citation - Scopus: 68On the Concept of Spectral Singularities(indian Acad Sciences, 2009) Guseinov, Gusein ShIn this paper, we discuss the concept of spectral singularities for non-Hermitian Hamiltonians. We exihibit spectral singularities of some well-known concrete Hamiltonians with complex-valued coefficients.
