论文标题
关于受限本征函数的广义傅里叶系数的增长
On the growth of generalized Fourier coefficients of restricted eigenfunctions
论文作者
论文摘要
令$（m，g）$为平滑，紧凑，riemannian歧管，$ \ {ϕ_h \} $ $ l^2 $ normalialized laplace eigenfunctions的序列$ m $。对于平滑的子曼福尔德$ h \子集M $，我们考虑通过在$ h $ wavefront Set上避免$ s^*h $的函数$ \ {ψ_h\} $测试限制的特征functions $ ϕ_H | _h $的增长。也就是说，我们研究所谓的广义傅里叶系数：$ \ langle ϕ_h，ψ_h\ rangle_ {l^2（h）} $。我们对这些系数进行明确绑定，这取决于两个功能的缺陷度量$ ϕ_h $和$ψ_H$相关的措施。这使我们可以在$ψ_H$的波前集合集合的复发方向集合时，可以得到一些$ -O $的改进。为了获得我们的估计值，我们利用了测量光束技术。
Let $(M,g)$ be a smooth, compact, Riemannian manifold and $\{ϕ_h\}$ a sequence of $L^2$-normalized Laplace eigenfunctions on $M$. For a smooth submanifold $H\subset M$, we consider the growth of the restricted eigenfunctions $ϕ_h|_H$ by testing them against a sequence of functions $\{ψ_h\}$ on $H$ whose wavefront set avoids $S^*H$. That is, we study what we call the generalized Fourier coefficients: $\langle ϕ_h,ψ_h\rangle_{L^2(H)}$. We give an explicit bound on these coefficients depending on how the defect measures for the two collections of functions $ϕ_h$ and $ψ_h$ relate. This allows us to get a little$-o$ improvement whenever the collection of recurrent directions over the wavefront set of $ψ_h$ is small. To obtain our estimates, we utilize geodesic beam techniques.
