微分算子D_θ的亚椭圆性

Hypoellipticity for Differential Operator D_θ

对算子Dθ在原点的亚椭圆性作了研究 .采用几个重要估计式来构造出Dθu=0的解u ,借助此解及相关理论 ,给出了算子Dθ 在原点亚椭圆的一个充分必要条件 .

In this paper, the hypoellipticity for operator D θ at the original is studied. Using some important estimations to construct the solution u for D θu=0,then depending on this solution and related theory, a sufficient and necessary condition of hypoellipticity for operator D θ at the original is presented.