Related papers: On a new inverse spectral problem
An integro-differential Dirac system with an integral term in the form of convolution is considered. We suppose that the convolution kernel is known a priori on a part of the interval, and recover it on the remaining part, using a part of…
We give a short review of results on inverse spectral problems for ordinary differential operators on a spatial networks (geometrical graphs). We pay the main attention to the most important nonlinear inverse problems of recovering…
In this study, the theorem on necessary and sufficient conditions for the solvability of inverse problem for Sturm-Liouville operator with discontinuous coefficient is proved and the algorithm of reconstruction of potential from spectral…
In this article, we study a boundary value problem of a class of singular linear discrete time systems whose coefficients are non-square constant matrices or square with a matrix pencil which has an identically zero determinant. By taking…
We prove that the resolvent of a linear operator pencil is analytic on an open annulus if and only if the coefficients of the Laurent series satisfy a system of fundamental equations and are geometrically bounded. Our analysis extends…
This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…
An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…
We study the inverse Sturm-Liouville problem on a finite interval from partial knowledge of spectral data. Specifically, we show that the potential can be uniquely reconstructed from the knowledge of a fraction of Dirichlet eigenvalues…
The operator of double differentiation, perturbed by the composition of the differentiation operator and a convolution one, on a finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability of recovering the…
We identify a class of operator pencils, arising in a number of applications, which have only real eigenvalues. In the one-dimensional case we prove a novel version of the Sturm oscillation theorem: if the dependence on the eigenvalue…
In this paper, we consider spectral problem for the nth order ordinary differential operator with degenerate boundary conditions. We construct a nontrivial example of boundary value problem which has no eigenvalues.
We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray…
Sum of a second derivative operator with periodic boundary conditions and an integral operator of rank one (non-local potential) is studied in this manuscript. Not only spectral analysis is conducted for this operator but the inverse…
We obtain a uniform stability of recovering entire functions of a special form from their zeros. To this form, one can reduce the characteristic determinants of strongly regular differential operators and pencils of the first and the second…
This article is concerned with uniqueness and stability issues for the inverse spectral problem of recovering the magnetic field and the electric potential in a Riemannian manifold from some asymptotic knowledge of the boundary spectral…
In the paper the conditions are obtained providing existence and uniqueness of the regular solution of the boundary problem for class of the second order homogeneous operator-differential equation with singular coefficients. High term of…
The general technique of derivation of Dubrovin's equation for the arbitrary operator pencils is suggested. The question of unique recovering of the finite-gap potential by coordinates of zeroes of the Psi-function is discussed. The crucial…
In this paper the complete spectral analysis of the operators is carried out and also with help of generalized normalizing numbers the inverse problem is solved.
We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…
The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and…