Related papers: Inverse spectral theory for perturbed torus
In this paper, we study the inverse spectral problem for the Sturm-Liouville operators on a star-shaped graph, which consists in the recovery of the potentials from specral data or several spectra. The uniform stability of these inverse…
This paper studies the inverse Steklov spectral problem for curvilinear polygons. For generic curvilinear polygons with angles less than $\pi$, we prove that the asymptotics of Steklov eigenvalues obtained in arXiv:1908.06455 determines, in…
This paper is concerned with the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of the differential expression coefficients from the spectral…
New high statistics data from the second generation of ultrarelativistic heavy-ion experiments open up new possibilities in terms of data analysis. To fully utilize the potential we propose to analyze the $m_\perp$-spectra of hadrons using…
In this paper, the Sturm-Liouville operators on a graph with a cycle are considered. We study the inverse spectral problem, which consists in the recovery of the potentials from several spectra and a sequence of signs related to the…
In this paper we consider two inverse problems on a closed connected Riemannian manifold $(M,g)$. The first one is a direct analog of the Gel'fand inverse boundary spectral problem. To formulate it, assume that $M$ is divided by a…
In this paper we study the behaviour of the continuous spectrum of the Laplacian on a complete Riemannian manifold of bounded curvature under perturbations of the metric. The perturbations that we consider are such that its covariant…
We consider a strongly damped wave equation on compact manifolds, both with and without boundaries, and formulate the corresponding inverse problems. For closed manifolds, we prove that the metric can be uniquely determined, up to an…
We study the questions of uniqueness and non-uniqueness for a pair of closely related inverse problems for the Bakry-\'Emery Laplacian $-\Delta_{\mathcal E}$ on a smooth compact and oriented Riemannian manifold with boundary…
Motivated by considerations of euclidean quantum gravity, we investigate a central question of spectral geometry, namely the question of reconstructability of compact Riemannian manifolds from the spectra of their Laplace operators. To this…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
We investigate linear parabolic maps on the torus. In a generic case these maps are non-invertible and discontinuous. Although the metric entropy of these systems is equal to zero, their dynamics is non-trivial due to folding of the image…
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…
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…
We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…
In this paper we study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from two spectra. We give a reconstruction algorithm and establish existence and uniqueness of reconstruction. Our approach…
In this paper, we study the amount of information contained in the Steklov spectrum of some compact manifolds with connected boundary equipped with a warped product metric. Examples of such manifolds can be thought of as deformed balls in…
We review basic ideas and basic examples of the theory of the inverse spectral problems.
In this work a spectral theory for 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation is developed. Spectral data for such solutions are defined (following Hitchin and Bobenko) and the space of spectral…
We consider an inverse spectral problem for a class of singular AKNS operators $H\_a, a\in\N$ with an explicit singularity. We construct for each $a\in\N$, a standard map $\lambda^a\times\kappa^a$ with spectral data $\lambda^a$ and some…