逆谱问题是几何分析和数学物理中最重要的问题之一，这个问题自1910年由著名物理学家H. A. Lorentz提出以来已经有一百多年的发展历史了。逆谱问题之所以引起人们的极大兴趣，一个最主要的原因是与逆谱问题密切相关的一大批分析问题、几何问题及数学物理问题具有深刻的理论背景和相当广泛的应用。本项目的研究内容包括三个部分：1) 给出（相应于Stokes不可压缩流体方程的）Stokes算子的一般逆谱展开公式；2） 给出(相应于弹性力学方程的)Lame算子的一般逆谱展开公式；3） 给出（相应于Maxwell电磁场方程的）Maxwell算子的一般逆谱展开公式。并进一步算出相应展开式的尽可能多的精确系数表达式。通过这些展开公式及精确系数来揭示这些基本数学物理方程背后所隐藏的深刻物理现象和规律。

Inverse spectrum problem is one of the most important problems in geometric analysis and mathematical physics, which has been developed for more than one hundred years since it was proposed by physicist H. A. Lorentz in 1910. Inverse spectral problems have aroused great interest, a most main reason is that the inverse spectral problems are closely related to a large number of problems on analysis, geometry and mathematical physics, and have profound theoretical background and a wide range of applications. The research content of this project includes three parts: 1) try to give precise inverse spectral expansion formula for Stokes operator that corresponds to Stokes fluid equations; 2） try to give precise inverse spectral expansion formula for the Lame operator which corresponds to the Lame elastic mechanics equations; 3） try to give inverse spectral expansion formula for the Maxwell operator which corresponds to the Maxwell electromagnetic field equations. Futhermore, we hope to calculate the exact coefficients of corresponding expansion expressions as much as possible. By these formulas and the exact coefficients, the profound physical phenomena and laws hidden behind these basic mathematical physics equations are revealed.