论文标题
全球溶解度和正规总和在紧凑的歧管上的常规性的传播
Global solvability and propagation of regularity of sums of squares on compact manifolds
论文作者
论文摘要
我们研究了在平滑函数和Schwartz分布的框架内，研究了在紧凑型Riemannian歧管$ t \ times g $上定义的矢量场的某些平方，其中进一步假定$ g $是谎言组。就像作者最近的一篇文章一样，我们的分析是根据与正在研究的操作员自然相关的$ g $的左右矢量字段的系统进行的，这是一个更简单的对象，尽管如此，它仍然传达了有关原始操作员的足够信息，以便完全编码其溶解度。作为为我们的主要目的而开发的工具的欢迎副作用，我们很容易地证明了对此类运营商的规律性传播的总体结果。
We investigate global solvability, in the framework of smooth functions and Schwartz distributions, of certain sums of squares of vector fields defined on a product of compact Riemannian manifolds $T \times G$, where $G$ is further assumed to be a Lie group. As in a recent article due to the authors, our analysis is carried out in terms of a system of left-invariant vector fields on $G$ naturally associated with the operator under study, a simpler object which nevertheless conveys enough information about the original operator so as to fully encode its solvability. As a welcome side effect of the tools developed for our main purpose, we easily prove a general result on propagation of regularity for such operators.
