摘要
本文给出了 Heisenberg 群 Hn 上增生算子的概念和构造方法,并利用增生算子方法得到了 Hn上一些左不变微分算子为亚椭圆算子的条件。
In this paper we give out a new concept named supplemental opera-tor of a left invariant differential operator on the Heisenberg group Hn.We prove that a left invariant differential operator on Hn is hypoellip-tie if It has a hypoelliptic supplemental operator on Hn(?)R^1 and wegive out a method to construct the supplemental operators.Moreover,with the aid of the supplemental operators we obtain some conditions ofhypoellipticity for a number of left invariant differential operators on Hn.Especially we prove that the operatorSum from j=1 to n (X_j^(4m1)+iY_j^(4m1))Sum from k=1 to n (X_k^(4m2)-iy_k^(4m2))+αt^2(m_1+m_2)+βis hypoelliptic on Hn if either m_1+m_2 is an even number and Reα≥0 orm_1+m_2 is odd and Reα≤0.Where m_1,m_2 are positive integers,βisarbitrary complex number and X_j,Y_j,T are bases of the left invariantvector field on Hn.
出处
《兰州大学学报（自然科学版）》
CAS
CSCD
北大核心
1989年第4期24-32,共9页
Journal of Lanzhou University(Natural Sciences)
基金
国家自然科学基金资助的课题
关键词
增生算子
Heisenbrg群
亚椭圆性
hypoellipticity
supplemental operator
Heisenberg group
left invariant differential operator
