Related papers: An Inverse Problem for Trapping Point Resonances

In this paper, we consider Schr\"odinger operators on $L^2(0,\infty)$ given by \begin{align} Hu=(H_0+V)u=-u^{\prime\prime}+V_0u+Vu,\nonumber \end{align} where $V_0$ is real, $1$-periodic and $V$ is the perturbation. It is well known that…

For a class of Riemannian manifolds with boundary that includes all negatively curved manifolds with strictly convex boundary, we establish H\"older type stability estimates in the geometric inverse problem of determining the electric…

This study explores the reconstruction of a signal using spectral quantities associated with some self-adjoint realization of an h-dependent Schr\"odinger operator when the parameter h tends to 0. Theoretical results in semi-classical…

We prove that a compactly supported perturbation of a rational or simply periodic algebro-geometric potential of the one-dimensional Schr\"odinger equation on the half line is uniquely determined by the location of its Dirichlet eigenvalues…

In this paper, we study for the first time the stability of the inverse source problem for the biharmonic operator with a compactly supported potential in $\mathbb R^3$. Firstly, to connect the boundary data with the unknown source, we…

In this article we improve some of the inverse spectral results proved by Guillemin and Uribe in \cite{GU}. They proved that under some symmetry assumptions on the potential $V(x)$, the Taylor expansion of $V(x)$ near a non-degenerate…

We apply recent results on semi-classical trace formulae and on Birkhoff normal forms for semi-classical Fourier integral operators to a wide range of semi-classical and high energy spectral inverse problems.

This paper is devoted to the study of a semiclassical "black box" operator $P$. We estimate the norm of its resolvent truncated near the trapped set by the norm of its resolvent truncated on rings far away from the origin. For $z$ in the…

We study the recovery of a spatially dependent source in a one-dimensional space-time fractional wave equation using boundary measurement data collected at a single endpoint. The main challenge arises from the fact that the eigenfunctions…

Let -Delta+V be the Schrodinger operator acting on L^2(R^d,C) with d odd larger than 2. Here V is a bounded real- or complex-valued function vanishing outside the closed ball of center 0 and radius a. If V belongs to the class of potentials…

We prove upper bounds on the number of resonances and eigenvalues of Schr\"odinger operators $-\Delta+V$ with complex-valued potentials, where $d\geq 3$ is odd. The novel feature of our upper bounds is that they are \emph{effective}, in the…

We consider the Schr\"odinger operator $H$ on the half-line with a periodic potential $p$ plus a compactly supported potential $q$. For generic $p$, its essential spectrum has an infinite sequence of open gaps. We determine the asymptotics…

We obtain semiclassical resolvent estimates for the Schr{\"o}dinger operator (ih$\nabla$ + b)^2 + V in R^d , d $\ge$ 3, where h is a semiclassical parameter, V and b are real-valued electric and magnetic potentials independent of h. Under…

In this article, we consider the semiclassical Schr\"odinger operator $P = - h^{2} \Delta + V$ in $\mathbb{R}^{d}$ with confining non-negative potential $V$ which vanishes, and study its low-lying eigenvalues $\lambda_{k} ( P )$ as $h \to…

Let P be the operator $-\Delta+V$ on R^d, where $V$ is a real potential with several inverse square singularities. The usual non-trapping type high-frequency inequality on the truncated resolvent of $P$ is shown, using semi-classical…

We investigate a two-dimensional Schr\"odinger operator, $-h^2 \Delta +iV(x)$, with a purely complex potential $iV(x)$. A rigorous definition of this non-selfadjoint operator is provided for bounded and unbounded domains with common…

We consider a general class of infinite dimensional reversible differential systems. Assuming a non resonance condition on the linear frequencies, we construct for such systems almost invariant pseudo norms that are closed to Sobolev-like…

We show that on a simple Riemannian manifold, the electric potential and the solenoidal part of the magnetic potential appearing in the magnetic Schr\"odinger operator can be recovered H\"older stably from the boundary spectral data. This…

For a large class of semiclassical pseudodifferential operators, including Schr\"odinger operators, $ P (h) = -h^2 \Delta_g + V (x) $, on compact Riemannian manifolds, we give logarithmic lower bounds on the mass of eigenfunctions outside…

The inverse scattering problem for the Schr$\mathrm{\ddot{o}}$dinger operators on the line is considered when the potential is real valued and integrable and has a finite first moment. It is shown that the potential on the line is uniquely…