Browsing by Author "Bairamov, Elgiz"

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Citation - WoS: 7
Citation - Scopus: 7
Fourth Order Differential Operators With Distributional Potentials
(Tubitak Scientific & Technological Research Council Turkey, 2020) Bairamov, Elgiz; Ugurlu, Ekin
In this paper, regular and singular fourth order differential operators with distributional potentials are investigated. In particular, existence and uniqueness of solutions of the fourth order differential equations are proved, deficiency indices theory of the corresponding minimal symmetric operators are studied. These symmetric operators are considered as acting on the single and direct sum Hilbert spaces. The latter one consists of three Hilbert spaces such that a squarely integrable space and two spaces of complex numbers. Moreover all maximal self-adjoint, maximal dissipative and maximal accumulative extensions of the minimal symmetric operators including direct sum operators are given in the single and direct sum Hilbert spaces.
Citation - WoS: 3
Citation - Scopus: 3
On Dirichlet-Integrable Solutions of Left-Definite Hamiltonian Systems
(Springer int Publ Ag, 2023) Bairamov, Elgiz; Ugurlu, Ekin
This paper aims to share a method to handle left-definite Hamiltonian systems and to construct nested-ellipsoids related with the corresponding hermitian forms. We share a lower bound for the number of linearly independent Dirichlet-integrable solutions of the Hamiltonian systems with respect to some nonnegative matrices. Moreover, we share the corresponding Titchmarsh-Weyl functions. At the end of the paper we introduce a limit-point criterion.
Citation - WoS: 3
Citation - Scopus: 3
On the Characteristic Functions and Dirchlet-Integrable Solutions of Singular Left-Definite Hamiltonian Systems
(Taylor & Francis Ltd, 2024) Ugurlu, Ekin; Bairamov, Elgiz; Tas, Kenan
In this work, a singular left-definite Hamiltonian system is considered and the characteristic-matrix theory for this Hamiltonian system is constructed. Using the results of this theory we introduce a lower bound for the number of Dirichlet-integrable solutions. Moreover we share a relation between the kernel of the solution of the nonhomogeneous boundary value problem and the characteristic-matrix.
On the Maximal Subspaces of Discrete Hamiltonian Systems
(Springernature, 2024) Bairamov, Elgiz; Ugurlu, Ekin
In this paper, we consider a discrete Hamiltonian system on nonnegative integers, and using Sylvester's inertia indices theory, we construct maximal subspaces on which the Hermitian form has a certain sign. After constructing nested ellipsoids, we introduce a lower bound for the number of linearly independent summable-square solutions of the discrete equation. Finally, we provide a limit-point criterion.
Citation - WoS: 5
Citation - Scopus: 5
The Spectral Analysis of a Nuclear Resolvent Operator Associated With a Second Order Dissipative Differential Operator
(Springer Heidelberg, 2017) Bairamov, Elgiz; Ugurlu, Ekin
In this paper, we introduce a new approach for the spectral analysis of a linear second order dissipative differential operator with distributional potentials. This approach is related with the inverse operator. We show that the inverse operator is a non-selfadjoint trace class operator. Using Lidskii's theorem, we introduce a complete spectral analysis of the second order dissipative differential operator. Moreover, we give a trace formula for the trace class integral operator.