Related papers: Reconstruction of the Dirac-Type Integro-Different…
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…
This paper is concerned with inverse spectral problems for higher-order ($n > 2$) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either…
Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…
We consider a Dirac-type operator $D_P$ on a vector bundle $V$ over a compact Riemannian manifold $(M,g)$ with a nonempty boundary. The operator $D_P$ is specified by a boundary condition $P(u|_{\p M})=0$ where $P$ is a projector which may…
We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their…
The operator of double differentiation on a finite interval with Robin boundary conditions perturbed by the composition of a Volterra convolution operator and the differentiation one is considered. We study the inverse problem of recovering…
In this paper, we develop two approaches to investigation of inverse spectral problems for a new class of nonlocal operators on metric graphs. The Laplace differential operator is considered on a star-shaped graph with nonlocal integral…
The spectral properties of Dirac operators on $(0,1)$ with potentials that belong entrywise to $L_p(0,1)$, for some $p\in[1,\infty)$, are studied. The algorithm of reconstruction of the potential from two spectra or from one spectrum and…
We study the inverse spectral problems of recovering Dirac-type functional-differential operator with two constant delays $a_1$ and $a_2$ not less than one-third of the interval. It has been proved that the operator can be recovered…
This paper addresses inverse spectral problems associated with Dirac-type operators with a constant delay, specifically when this delay is less than one-third of the interval length. Our research focuses on eigenvalue behavior and operator…
We study the non-selfadjoint Dirac system on a finite interval having non-integrable regular singularities in interior points with additional matching conditions at these points. Properties of spectral characteristics are established, and…
We consider a variable order differential operator on a graph with a cycle. We study the inverse spectral problem for this operator by the system of spectra. The main results of the paper are the uniqueness theorem and the constructive…
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…
The inverse problem for the differential operator pencil with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator…
We establish uniqueness and stability inequalities for the problem of determining the higher-order coefficients of an elliptic operator from the corresponding boundary spectral data (BSD). Our analysis relies on the relationship between…
This article shows that knowledge of the Dirichlet-Neumann map on certain subsets of the boundary for input functions supported roughly on the rest of the boundary can be used to determine a magnetic Schr\"{o}dinger operator. With some…
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 paper, a diffusion operator including conformable fractional derivatives of order {\alpha} ({\alpha} in (0,1)) is considered. The asymptotics of the eigenvalues, eigenfunctions and nodal points of the operator are obtained.…
This note introduces a regression technique for finding a class of nonlinear integro-differential operators from data. The method parametrizes the spatial operator with neural networks and Fourier transforms such that it can fit a class of…
In this paper, we consider the recovery of third-order differential operators from two spectra, as well as fourth-order or fifth-order differential operators from three spectra, where these differential operators are endowed with…