spectrum

Recovering singular differential pencils with a turning point

Authors: Yurko V. A.

Second-order pencils of differential equations on the half-line with turning points are considered. We establish properties of the spectrum and study the inverse spectral problem of recovering coefficients of the pencil from the spectral data.

The Il’in Spectral Method for Determination of the Properties of the Basis Property and the Uniform Convergence of Biorthogonal Expansions on a Finite Interval

Authors: Lomov I. S.

The paper discusses the basics of the spectral method of V. A. Il’in on an example of a simple second order differential operator on a segment of the number line. The first theorem of Il’in on the unconditional basis property is stated. Its detailed proof is given. A chain of generalizations of this theorem is traced. A recently established a theorem on the unconditional basis property for the differential operators with general integral boundary conditions is formulated.

Numerical Investigation of Spectrums of Three-Dimensional Turbulent Convection

Authors: Palymskiy I. B.

The three-dimensional turbulent convectional flows of viscous and incompressible fluid in a rectangular parallelepiped numerically is simulated at heating from below. The horizontal boundaries are stress-free and isothermal. The calculated time spectrum of temperature pulsations at supercriticality is equal to 410 in centre of convective cell has a good agreement with experimental data for convection in cryogenic He. The Obukhov – Bolgiano spectra k−11/5, k−3 and k−5 have been found for velocity pulsations.

Solution of Inverse Problem for the Diffusion Operator in a Symmetric Case

Authors: Nabiev I.

In the paper uniqueness of reconstruction of the diffusion operator by aspectrum is proved and sufficient solvability conditions are provided.

Spectral Analysis of a Class of Difference Operators with Growing Potential

Authors: Garkavenko G. V., Uskova N. B.

The similar operator method is used for the spectral analysis of the closed difference operator of the form (A x)(n) = x(n + 1) + x(n − 1) − 2x(n) + a(n)x(n), n ∈ Z under consideration in the Hilbert space l2(Z) of bilateral sequences of complex numbers, with a growing potential a : Z → C. The asymptotic estimates of eigenvalue, eigenvectors, spectral estimation of equiconvergence applications for the test operator and the operator of multiplication by a sequence a : Z → C.

On spectrum of some classes of matrix operators

Authors: Ismailov M. I.

The paper is devoted to investigation of the spectrum of some classes of matrix operators. The relations between the parts of the spectrum of the matrix operators with corresponding parts of its elements are established. 

Dirac System with Undifferentiable Potential and Antiperiodic Boundary Conditions

Authors: Kornev V. V., Khromov A. P.

The object of the paper is Dirac system with antiperiodic boundary conditions and complex-valued conditions potential. A new method

is suggested for investigating spectral properties of this boundary problem. The method is based on the formulas of the transform

operators type. It is rather elementary and simple. Using this method asymptotic behaviour of eigenvalues is specificated and it is

proved that eigen and associated functions form Riesz basis with brackets in the space of quadratic summerable two-dimensional