Spectra of domains in compact manifolds
Spectra of domains in compact manifolds
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DOI：
10.1016/0022-1236(78)90070-8
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发表时间：
1978-11
影响因子：
1.7
通讯作者：
I. Chavel;E. Feldman
中科院分区：
文献类型：
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作者：
I. Chavel;E. Feldman
2000 CHAVEL AND FELDMAN与H相关的投影算子。如定理1，令0< h,(T)< A？(T)<***表示多重计数的X-Q (T)上边值问题的特征值，（~ JJ~(T), &T），…}由{/J (T), a,(T)，…的ezgenfunctions组成的(f E L2 (X): f 1q (T)= 0 >的完备标准正交基分别}。对于每个I= 1,2，…设H，(T)是由向量张成的fl2 (X)的子空间，设Pz (,): L2 (X)-+ L2 (X)是与Hz（~）相关的投影算子。然后对于所有1= 1,2，…对于非一般情况的更详细的信息，我们将自己限制在经典情况下，其中X是一个空间形式，即一个紧单连通的1阶黎曼对称空间，或者更具体地说，是22维的标准球面。对于对称空间
200 CHAVEL AND FELDMAN the projection operator associated with H,. As in Theorem 1 let0< h,(T)< A?(T)<*** denote the eigenvalues of the boundary value problem on X-Q (T) counted with multiplicity, and (~ JJ~(T), &T),...} a complete orthonormal basis of (f E L2 (X): f 1 Q (T)= O> consisting of ezgenfunctions of {/J (T), A,(T),...}, respectively. For each I= 1, 2,... let H,(T) be the subspace ofL2 (X) spanned by the vectors and let Pz (,): L2 (X)-+ L2 (x) be the projection operator associated with Hz (~). Then for all 1= 1, 2,... we haveFor more detailed information in the nongeneric case we restrict ourselves to the classical case where X is a space form, viz., a compact simply connected Riemannian symmetric space of rank one, or more particularly, the standard sphere of dimension 22. For the symmetric spaces we have