二步幂零李群H_(2n+1)×R^(2d)上一类非齐次非横截椭圆不变微分算子的显式基本解  

EXPLICIT FUNDAMENTAL SOLUTIONS FOR ONE CLASS OF NONHOMOGENEOUS NONTRANSVERSALLY ELLIPTIC DIFFERENTIAL OPERATORS ON THE TWO STEP NILPOTENT GROUP H 2n+1 ×R 2d

作　　者：何春雄[1] 俞建宁[2] 

机构地区：[1]中科院兰州冰川冻土研究所冻土工程国家重点试验室 [2]兰州铁道学院

出　　处：《纯粹数学与应用数学》1997年第2期12-19,共8页Pure and Applied Mathematics

基　　金：国家自然科学基金

摘　　要：用随机分析方法，我们构造出了二步幂零李群Ｈ２ｎ＋１×Ｒ２ｄ上的一类非齐次非横截椭圆不变微分算子的显式基本解，并在此基础上讨论了它们的局部可解性和亚椭圆性．In this paper, using the stochastic methods, we constructed explicit fundamental solutions for one class of nonhomogeneous nontransversally elliptic differential operators on the two step nilpotent group H 2n+1 ×R 2d , and discussed the hypoellipticity and local solvability of the operators. The general form of the operators are as follows 12∑nj=1a jL 2 j+∑nj=1α jM j+12∑dk=1b kU 2 k+∑dk=1β kV k+γT here, L 1,L 2,…,L n,M 1,M 2,…,M n and T are left invariant vector fields on H 2n+1 . U k,V k,k=1,2,…,d are left invariant vector fields on R 2d . a j>0 is real and Re α j>0,j=1,2,…,n. b k>0 is real and Re β k>0, k=1,2,…,d. γ is complex and there is a r 10 such that γ=r 1α 1.

关 键 词：不变微分算子 基本解 幂零李群 微分算子 

分 类 号：O175.3[理学—数学]