H型群上次Laplace算子相邻特征值之差的估计  

Estimates for the differences of consecutive eigenvalues of the sub-Laplacian on groups of H type

作　　者：韩军强[1] 钮鹏程[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072

出　　处：《西北大学学报（自然科学版）》2006年第4期522-524,共3页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(10371099)

摘　　要：目的研究H型群G上次Laplace算子的D irichlet特征值问题。方法建立H型群G上向量场的性质,结合欧氏空间的经典方法。结果给出了H型群G上次Laplace算子D irichlet特征值问题相邻特征值之差的估计,此结果与区域的几何和G的Lie代数的第二层的维数无关。结论把欧氏空间上的结论推广到了H型群上,并在H型群情形下有所深化。Aim To study the Dirichlet eigenvalue problem of the sub-Laplacian on groups of H type, G. Methods Establish properties of vector fields on groups of H type and combine the classical methods in the Euclidean spaces. Results The estimates for the differences of consecutive eigenvalues of the Dirichlet eigenvalue problem of the sub- Laplacian on groups of H type, G, are given. The results here are independent of the geometry of the domain and the dimension of the second layer of Lie algebra of G. Conclusion The conclusions in the Euclidean spaces are generalized to groups of H type and are deepen.

关 键 词：H型群 次LAPLACE算子 特征值 估计 

分 类 号：O175.2[理学—数学]