Elgiz Bairamov

The determinants of dissipative Sturm-Liouville operators with transmission conditions

In this paper, we study the determinant of perturbation connected with the dissipative operator L generated in L^2(I) by (1.1)-(1.5). Then using Livsics theorem, we investigate the problem of completeness of the system of eigenfunctions and associated functions of L.

Spectral Analysis of Non‐Selfadjoint Discrete Schrödinger Operators with Spectral Singularities

Let L denote the non-selfadjoint discrete Schrodinger operator generated in 2(ℕ) by the difference expression (y)n = yn –1 + yn + 1 + bnyn, n ∈ ℕ = {1, 2, …,} and the boundary condition y0 = 0, where {bn}∞n = 1 is a complex sequence. In this paper we investigate Weyl-Titchmarsh (W – T ) function of the operator L and obtained the relation between W – T function and the generalized spectral function of L in the sense of Marchenko. Moreover we find Cauchy type integral representation of W – T function. Using this representation we derived the spectral expansion of L in terms of the principal vectors, taking into account the spectral singularities.

An eigenvalue problem for quadratic pencils of q-difference equations and its applications

Abstract This work is devoted to the study of the properties of eigenvalues and eigenvectors of a quadratic pencil of q -difference equations. The results obtained are then used to solve the corresponding system of differential equations with boundary and initial conditions.

Dissipative operators with impulsive conditions

In this paper a singular dissipative impulsive boundary value problem with

On the characteristic values of the real component of a dissipative boundary value transmission problem

n

Jost Solution and the Spectrum of the Discrete Dirac Systems

-impulsive points is investigated. In particular, using the Lidskiĭ’s theorem it is proved that all eigen and associated functions of this problem is complete in the Hilbert space.

The structure of the spectrum of a system of difference equations

Abstract In this paper using the uniqueness theorem of analytic functions we investigated the eigenvalues and the spectral singularities of the difference equation a n−1 y n−1 +b n y n +a n y n+1 =λy n , n∈ Z ={0,±1,±2,…}, where t{a n } n∈ Z , {b n } n∈ Z are complex sequences and λ is a spectral parameter.

Krein's Theorem for the Dissipative Operators with Finite Impulsive Effects

Abstract In this paper, using Krein’s theorem, we investigate the completeness of the system of root vectors of a Bessel-type singular dissipative boundary value transmission problem in the Weyl’s limit circle case.