论文标题
正方金和紧凑型歧管上的全球不动脉
Global hypoellipticity of sums of squares on compact manifolds
论文作者
论文摘要
在这项工作中，我们为正方形类型的操作员提供了必要和充分的条件。这些新条件涉及矢量场系统的全球性低纤维化性，并且比Hörmander的条件弱，同时它们将众所周知的二磷剂条件推广到圆环上。我们还能够提供在一般环境中满足这些条件的操作员的示例。
In this work, we present necessary and sufficient conditions for an operator of the type sum of squares to be globally hypoelliptic on a product of compact Riemannian manifolds $T \times G$, where $G$ is also a Lie group. These new conditions involve the global hypoellipticity of a system of vector fields and are weaker than Hörmander's condition, at the same time that they generalize the well known Diophantine conditions on the torus. We were also able to provide examples of operators satisfying these conditions in the general setting.
