Related papers: Inverse spectral problems on a closed manifold

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…

Let $L_0$ be a closed densely defined symmetric semi-bounded operator with nonzero defect indexes in a separable Hilbert space ${\cal H}$. With $L_0$ we associate a metric space $\Omega_{L_0}$ that is named a {\it wave spectrum} and…

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…

We study inverse boundary problems for magnetic Schr\"odinger operators on a compact Riemannian manifold with boundary of dimension $\ge 3$. In the first part of the paper we are concerned with the case of admissible geometries, i.e.…

We consider inverse problems for wave, heat and Schr\"odinger-type operators and corresponding spectral problems on domains of ${\bf R}^n$ and compact manifolds. Also, we study inverse problems where coefficients of partial differential…

After formulating the pressure wave equation in half-space minus a crack with a zero Neumann condition on the top plane, we introduce a related inverse problem. That inverse problem consists of identifying the crack and the unknown forcing…

We consider inverse problems consisting of the reconstruction of an unknown signal $f$ from noisy measurements $y=Ff+\text{noise}$, where $Ff$ is a function on a Riemannian manifold without boundary $\mathcal M$. We consider the case when…

For a closed Riemannian orbifold $O$, we compare the spectra of the Laplacian, acting on functions or differential forms, to the Neumann spectra of the orbifold with boundary given by a domain $U$ in $O$ whose boundary is a smooth manifold.…

Let (M,g,J) be a compact Hermitian manifold with a smooth boundary. Let $\Delta_p$ and $D_p$ be the realizations of the real and complex Laplacians on p forms with either Dirichlet or Neumann boundary conditions. We generalize previous…

In this paper, we establish positive results for two spectral inverse problems in the presence of a magnetic potential. Exploiting the principal wave trace invariants, we first observe that on closed Anosov manifolds with simple length…

This work deals with an inverse problem for the Sturm-Liouville operator with non-separated boundary conditions, one of which linearly depends on a spectral parameter. Uniqueness theorem is proved, solution algorithm is constructed and…

With a densely defined symmetric semi-bounded operator of nonzero defect indexes $L_0$ in a separable Hilbert space ${\cal H}$ we associate a topological space $\Omega_{L_0}$ ({\it wave spectrum}) constructed from the reachable sets of a…

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 study two inverse problems on a globally hyperbolic Lorentzian manifold $(M,g)$. The problems are: 1. Passive observations in spacetime: Consider observations in a neighborhood $V\subset M$ of a time-like geodesic $\mu$. Under natural…

Let $(M,g)$ be a closed Riemannian manifold. The aim of this work is to prove the Lebeau-Robbiano spectral inequality for a positive elliptic pseudo-differential operator $E(x,D)$ on $M,$ of order $\nu>0,$ in the H\"ormander class…

We solve a spectral and an inverse spectral problem arising in the computation of peakon solutions to the two-component PDE derived by Geng and Xue as a generalization of the Novikov and Degasperis-Procesi equations. Like the spectral…

This article is about two types of restrictions of eigenfunctions $\phi_j$ on a compact Riemannian manifold $(M,g)$: First, we restrict to a submanifold $H \subset M$, and expand the restriction $\gamma_H \phi_j$ in eigenfunctions $e_k$ of…

We solve the inverse spectral problem for rotationally symmetric manifolds, which include the class of surfaces of revolution, by giving an analytic isomorphism from the space of spectral data onto the space of functions describing the…

On the half line $[0,\infty)$ we study first order differential operators of the form $B 1/i d/(dx) + Q(x)$, where $B:=\mat{B_1}{0}{0}{-B_2}$, $B_1,B_2\in M(n,\C)$ are self--adjoint positive definite matrices and $Q:\R_+\to M(2n,\C)$,…

If $(M,g)$ and $(\hM,\hg)$ are two smooth connected complete oriented Riemannian manifolds of dimensions $n$ and $\hn$ respectively, we model the rolling of $(M,g)$ onto $(\hM,\hg)$ as a driftless control affine systems describing two…