该文给出了拟齐次线性偏微分算子P(x,D)在原点为解析亚椭圆的一个必要条件: 若u∈S~’_(μ,λ)(R~n), 且Pu＝0, 则存在整函数v, Pv＝0, v和u在x＝0的某个邻域中重合.

This paper gives a necessary condition for a linear partial differential operator P(x,D), which is homogeneous with respect to some dilations, to be analytic hypoelliptic at the origin as follows: Assume u implied by S'_(#mu#,#lambda#)(R~n)(for S'_(#mu#,#lambda#)R~n, see Introduction) and Pu=0. Then there exists an entire function v satisfying Pv=0 where v is consistent with u in some neighborhood of x=0.