Fundamental solutions for a class of hypoelliptic PDE
Fundamental solutions for a class of hypoelliptic PDE
复制标题
DOI：
10.1090/s0002-9947-1980-0554324-x
复制
发表时间：
1980
影响因子：
9.2
通讯作者：
A. Kaplan
中科院分区：
文献类型：
--
作者：
A. Kaplan
我们引入一类幂零李群自然产生的概念组成的二次型，并表明，他们的标准sublaplacian承认基本解决方案类似于已知的海森堡群。根据Hormander [6]的定理，如果XI，...，X，是流形N上的向量场，具有这样的性质，即它们的直到一定阶的算子在每一点上都跨越切空间，则微分算子
We introduce a class of nilpotent Lie groups which arise naturally from the notion of composition of quadratic forms, and show that their standard sublaplacians admit fundamental solutions analogous to that known for the Heisenberg group. By a theorem of Hormander [6], if XI, ... , X, are vector fields on a manifold N with the property that their commutators up to a certain order span the tangent space at every point, then the differential operator