Related papers: Periodic and almost periodic potentials in the inv…
In this work we present a semi-classical approach to solve the inverse spectrum problem for one-dimensional wave equations for a specific class of potentials that admits quasi-stationary states. We show how inverse methods for potential…
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…
Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…
We study the inverse scattering problem for electric potentials and magnetic fields in $\ere^d, d\geq 3$, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from…
We develop direct and inverse scattering theory for one-dimensional Schroedinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete…
We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0,2\pi)$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As an inverse data we use a…
This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…
Inverse scattering theory is extended to one-dimensional Schr\"odinger problems with near-boundary singularities of the form $v(z\to 0)\simeq -z^{-2}/4+v_{-1}z^{-1}$. Trace formulae relating the boundary value $v_0$ of the nonsingular part…
We study the spectral theory and inverse problem on asymptotically hyperbolic manifolds. The main subjects are as follows: (1)Location of the essential spectrum. (2)Absence of eigenvalues embedded in the continuous spectrum. (3)Limiting…
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…
Inverse spectral problem for a self-adjoint differential operator, which is the sum of the operator of the third derivative on a finite interval and of the operator of multiplication by a real function (potential), is solved. Closed system…
This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…
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 consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator…
The inverse problem for the Sturm- Liouville operator 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 is…
In this work, we consider Dirac-type operators with a constant delay less than two-fifths of the interval and not less than one-third of the interval. For our considered Dirac-type operators, an incomplete inverse spectral problem is…
Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.
This is a survey of the inverse spectral problem on (mainly compact) Riemannian manifolds, with or without boundary. The emphasis is on wave invariants: on how wave invariants have been calculated and how they have been applied to concrete…
In our article we consider some algebraical methods which may be useful in some inverse spectral problems. The reconstraction of the matrix from its minors is considered.
We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally…