Stability for the multi-dimensional Borg-Levinson theorem with partial spectral data

关于分数阶Borg-Levinson问题

On Fractional Borg-Levinson Problem

本文研究分数阶Borg-Levinson反谱问题，证明在容许类中势函数可由边界谱数据唯一确定，分数阶指数限于(1/2,1)，容许类仅依赖于区域和空间维度。

Stability for the multi-dimensional Borg--Levinson theorem of the biharmonic operator

In this paper, we prove a conditional Hölder stability estimate for the inverse spectral problem of the biharmonic operator. The proof employs the resolvent estimate and a Weyl-type law for the biharmonic operator which were obtained by the authors in \cite{LYZ}. This work extends nontrivially the result in \cite{stefanov} from the second order Schrödinger operator to the fourth order biharmonic operator.

A multidimensional Borg-Levinson theorem for magnetic Schrödinger operators with partial spectral data

We consider the multidimensional Borg-Levinson theorem of determining both the magnetic field $dA$ and the electric potential $V$, appearing in the Dirichlet realization of the magnetic Schrödinger operator $H=(-{\rm i}\nabla+A)^2+V$ on a bounded domain $Ω\subset\mathbb R^n$, $n\geq2$, from partial knowledge of the boundary spectral data of $H$. The full boundary spectral data are given by the set $\{(λ_{k},{\partial_νϕ_{k}}_{|\partialΩ}):\ k\geq1\}$, where $\{ λ_k:\ k\in \mathbb N^* \}$ is the non-decreasing sequence of eigenvalues of $H$, $\{ ϕ_k:\ k\in \mathbb N^* \}$ an associated Hilberti…

具有无界势的 Robin Laplacian 的多维 Borg-Levinson 唯一性与稳定性结果

Multidimensionnel Borg-Levinson uniqueness and stability results for the Robin Laplacian with unbounded potential

针对三维及以上有界区域中带 Robin 边界条件的 Schrödinger 算子，本文利用特征值与完整或部分边界 Dirichlet 测量组成的谱数据，研究无界势反演的 Borg-Levinson 唯一性与稳定性。

Application of the boundary control method to partial data Borg-Levinson inverse spectral problem

We consider the multidimensional Borg-Levinson problem of determining a potential $q$, appearing in the Dirichlet realization of the Schrödinger operator $A_q=-Δ+q$ on a bounded domain $Ω\subset \mathbb{R}^n$, $n\geq2$, from the boundary spectral data of $A_q$ on an arbitrary portion of $\partialΩ$. More precisely, for $γ$ an open and non-empty subset of $\partialΩ$, we consider the boundary spectral data on $γ$ given by $\mathrm{BSD}(q,γ):=\{(λ_{k},{\partial_νϕ_{k}}_{|\overlineγ}):\ k \geq1\}$, where $\{ λ_k:\ k \geq1\}$ is the non-decreasing sequence of eigenvalues of $A_q$, $\{ ϕ_k:\ k \geq…

Multidimensional Borg-Levinson Theorem

We consider the inverse problem of the reconstruction of a Schrödinger operator on a unknown Riemannian manifold or a domain of Euclidean space. The data used is a part of the boundary $Γ$ and the eigenvalues corresponding to a set of impedances in the Robin boundary condition which vary on $Γ$. The proof is based on the analysis of the behaviour of the eigenfunctions on the boundary as well as in perturbation theory of eigenvalues. This reduces the problem to an inverse boundary spectral problem solved by the boundary control method.

A Borg-Levinson theorem for magnetic Schrödinger operators on a Riemannian 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 data of the corresponding Schrödinger operator under Dirichlet boundary conditions. The spectral data consist of some asymptotic knowledge of a subset of eigenvalues and Neumann traces of the associated eigenfunctions of the magnetic Laplacian. We also address the same question for Schrödinger operators under Neumann boundary conditions, in which case we measur…

利用渐近边界谱数据确定双调和算子的一阶扰动

Determination of first order perturbation for bi-harmonic operator by asymptotic boundary spectral data

该研究针对有界光滑区域中的受扰双调和算子，证明可由 Dirichlet 特征值及特征函数 Neumann 迹的渐近边界谱数据稳定恢复其一阶与零阶系数。

从单次被动测量重构一维发展方程及其初始数据

Reconstruction of 1-D evolution equations and their initial data from one passive measurement

本文研究一维发展方程的被动测量反问题，通过建立与1D Schrödinger算子谱理论的联系，在无通用性假设下证明了波动和热传导方程系数与初始数据可被同时唯一确定。