On integrals of eigenfunctions over geodesics
On integrals of eigenfunctions over geodesics
复制标题
关于测地线上本征函数的积分
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
C. Sogge
中科院分区：
文献类型：
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作者：
Xuehua Chen;C. Sogge
If $(M,g)$ is a compact Riemannian surface then the integrals of $L^2(M)$-normalized eigenfunctions $e_j$ over geodesic segments of fixed length are uniformly bounded. Also, if $(M,g)$ has negative curvature and $gamma(t)$ is a geodesic parameterized by arc length, the measures $e_j(gamma(t)), dt$ on $R$ tend to zero in the sense of distributions as the eigenvalue $la_j o infty$, and so integrals of eigenfunctions over periodic geodesics tend to zero as $la_j o infty$. The assumption of negative curvature is necessary for the latter result.
