Microlocal analysis of topological Radon transforms and their application to singularity thoery

本文研究了可构造函数的积分变换，其积分理论是基于欧拉特征线的。证明了Grassmann流形上拓扑Radon变换的象满足一个拓扑积分方程组。注意在解析情形下图像满足一个偏微分方程组，我们还证明了可定义函数的拓扑Radon变换的反演公式，这比可构造函数更一般。

In this research, we study integral transforms of constructible functions, whose integral theory is based on the Euler characteristic. We proved that the images of topological Radon transforms on Grassmann manifolds satisfy a system of topological integral equations. Note that in the analytic case the images satisfy a system of partial differential equations.We also prove an inversion formula for topological Radon transforms of definable functions, which are more general than constructible functions.