The Poisson Summation Formula for Manifolds with Boundary
The Poisson Summation Formula for Manifolds with Boundary
复制标题
有边界流形的泊松求和公式
DOI：
10.1016/0001-8708(79)90042-2
复制
发表时间：
1979
影响因子：
1.7
通讯作者：
R. Melrose
中科院分区：
文献类型：
--
作者：
V. Guillemin;R. Melrose
对于紧致无边界黎曼流形X，存在一个Poisson型求和公式，它将X的长度谱与拉普拉斯算子的本征值联系起来.如果所有的闭测地线都是单测地线，并且它们的Maslov指数为零，则公式为：ccm（h）t = 2; Iyyi，l，lS（t-TJ $ R（1.1））IGpecd Y，其中E> 0。右边的和是在所有闭测地线上的，y; T，是y的周期，T，* 是y的本原周期，P，围绕y和R的庞加莱映射在&，，公式说，由左边的和定义的t的分布函数等于右边模的和局部I，-可和函数，[3]和[4]。
For a compact boundaryless Riemannian manifold X there is a Poisson-type summation formula which relates the Iength spectrum of X and the eigenvalues of the Laplace operator. If all closed geodesics are simple and their Maslov indices are zero the formuIa says: c cm (h)“‘t= 2; I yy;, l, lS (t-TJ $ R(1.1) liGpecd Y for E> 0. The sum on the right is over all closed geodesics, y; T, is the period of y, T,,* the primitive period of y, P, the Poincare map around y and R is in&,, The formula says that the distributional function of t defined by the sum on the left is equal to the sum on the right module locally I;,-summable functions,[3] and [4].