Necessary and Sufficient Conditions for the Solvability of Inverse Problem for a Class of Dirac Operators

In this paper, we consider a problem for the first order Dirac differential equations system with spectral parameter dependent in boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this system are investigated. The expansion formula with respect to eigenfunctions is obtained and Parseval equality is given. The main theorem on necessary and sufficient conditions for the solvabilty of inverse problem is proved and the algorithm of reconstruction of potential from spectral data (the sets of eigenvalues and normalizing numbers) is given.Comment: 19 page

On an Inverse Problem for a Class of Dirac Operator with Discontinuous Coefficient and a Spectral Parameter in the Boundary Condition

Abstract In this paper, it is examined on the half line the inverse problem of scattering theory for a class Dirac operator with discontinuous coefficient and a spectral parameter in the boundary condition . The scattering function is defined as scattering data and its properties are investigated. It is obtained Gelfand-Levitan-Marchenko type main equation which plays an important role in the solution of inverse problem and it is shown the uniqueness of the solution of the inverse problem by using Fredholm alternative. Mathematics Subject Classification: 34A55, 34B24, 34L0

Surface topography of the InSb-MnSb thin films

In that report we observe a semiconductor eutectic composite InSb-MnSb thin films, prepared by the "flash evaporation" method. The atomic force microscopy and the scanning electron microscopy were employed for investigation microstructure and surface relief of the InSb-MnSb thin films. В этом отчете мы наблюдаем за тонкими пленками полупроводникового электического композита InSb-MnSb, полученными методом «мгновенного испарения». С помощью атомно-силовой микроскопии и сканирующей электронной микроскопии исследованы микроструктура и рельеф поверхности тонких пленок InSb-MnSb

Surface topography of the InSb-MnSb thin films

In that report we observe a semiconductor eutectic composite InSb-MnSb thin films, prepared by the "flash evaporation" method. The atomic force microscopy and the scanning electron microscopy were employed for investigation microstructure and surface relief of the InSb-MnSb thin films. В этом отчете мы наблюдаем за тонкими пленками полупроводникового электического композита InSb-MnSb, полученными методом «мгновенного испарения». С помощью атомно-силовой микроскопии и сканирующей электронной микроскопии исследованы микроструктура и рельеф поверхности тонких пленок InSb-MnSb

On the inverse problem of the scattering theory for a class of systems of Dirac equations with discontinuous coefficient

In this paper it is devoted to study the inverse scattering problem for a singular boundary value problem of generalized form of system Dirac type. The new representation for the solutions of the differential equations system is considered, the scattering function is defined and its properties are given. The main equation is obtained for the solution of the inverse problem and it is shown the uniqueness of the solution of the inverse problem of scattering theory on the half lin

On the expansion formula for a class of Dirac operator with discontinuous coefficient

In this paper we consider a first order differential equation system with a discontinuous coefficient and spectral parameter dependent boundary condition in the half line. The operator interpretation of the given boundary value problem is investigated in the Hilbert space H = L2;½ ¡ 0;1;C2¢ £ C. The resolvent operator is constructed and the expansion formula with respect to eigenfunctions is obtaine

On an inverse problem for a class Dirac operator with discontinuous coefficient and a spectral parameter in the boundary condition

In this paper, it is examined on the half line the inverse problem of scattering theory for a class Dirac operator with discontinuous coefficient and a spectral parameter in the boundary condition . The scattering function is defined as scattering data and its properties are investigated. It is obtained Gelfand-Levitan-Marchenko type main equation which plays an important role in the solution of inverse problem and it is shown the uniqueness of the solution of the inverse problem by using Fredholm alternative