Decomposability of Nonnegative r-Potent Matrices

Decomposability of nonnegative r-potent operators on L2(X)

We investigate the decomposability of nonnegative compact r-potent operators on a separable Hilbert space L2(X). We provide a constructive algorithm to prove that basis functions of range spaces of nonnegative r-potent operators can be chosen to be all nonnegative and mutually orthogonal. We use this orthogonality to establish that nonnegative compact r-potent operators with range spaces of dimension strictly greater than r-1 are decomposable.

非负 Ricci 曲率非紧流形上的多孔介质方程：Green 函数方法

The porous medium equation on noncompact manifolds with nonnegative Ricci curvature: a Green function approach

本文针对非负 Ricci 曲率的完备非紧流形上的多孔介质方程，利用 Green 函数构造大于 L^1 的加权空间 X，证明弱对偶解存在性并给出尖锐光滑化估计。