Microlocalization of Resonant States and Estimates of the Residue of the Scattering Amplitude
Microlocalization of Resonant States and Estimates of the Residue of the Scattering Amplitude
复制标题
谐振态的微局域化和散射幅度残留的估计
DOI：
10.1007/s00220-004-1050-6
复制
发表时间：
2004
影响因子：
2.4
通讯作者：
L. Michel
中科院分区：
文献类型：
--
作者：
J. Bony;L. Michel
我们得到了与Anh-微分算子的共振态有关的微域估计。更准确地说，我们证明了归一化共振态在捕获轨迹集之外，并且在相空间的入射区域内。作为应用，我们证明了在谱投影器范数的估计下，薛定谔算子的散射振幅在某些方向上的剩余是小的。最后，我们在一些例子中证明了这个界。
We obtain some microlocal estimates of the resonant states associated to a resonancez0of anh-differential operator. More precisely, we show that the normalized resonant states are outside the set of trapped trajectories and are in the incoming area of the phase space. As an application, we show that the residue of the scattering amplitude of a Schrödinger operator is small in some directions under an estimate of the norm of the spectral projector. Finally we prove such a bound in some examples.