Mathematical Sciences: An Inverse Spectral Theory Problem for Bounded Domains in Two or More Dimensions

给出一个可以模拟物理系统的线性微分方程式，人们可以根据系数的知识来求解。这里要解决的问题是逆问题：给定一些解的知识，尝试确定特定的微分方程，从而确定潜在的物理系统。所提出的研究旨在基于研究者在一维问题上所取得的成功来处理二维或更多维的反问题。

Given a linear differential equation which may model a physical system one may seek the solutions based on a knowledge of the coefficients. The problem being addresses here is the inverse problem: Given some knowledge of the solutions try to determine the particular differential equation and hence the underlying physical system. The proposed research is directed to handle inverse problems in dimensions two or more based on the success achieved by the investigator with one-dimensional problems.