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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: 27Citation - Scopus: 39Properties of the Laplace transform on time scales with arbitrary graininess(Taylor & Francis Ltd, 2011) Bohner, Martin; Guseinov, Gusein Sh.; Karpuz, BasakWe 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.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: 3Citation - Scopus: 3Inverse Spectral Problem for Finite Jacobi Matrices With Zero Diagonal(Taylor & Francis Ltd, 2015) Aydin, Ayhan; Guseinov, Gusein Sh.In 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 - 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.
