Resonance free regions for nontrapping manifolds with cusps
Resonance free regions for nontrapping manifolds with cusps
复制标题
具有尖点的非俘获流形的无共振区域
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
K. Datchev
中科院分区：
文献类型：
--
作者：
K. Datchev
我们证明了具有尖点的非捕获流形的可解估计，这意味着存在任意宽的共振自由带，薛定谔方程的局部平滑和共振波展开。我们得到了无损的极限吸收和局部平滑估计，但全纯连续解的估计存在损失。我们证明了这些估计在某些方面是最优的。
We prove resolvent estimates for nontrapping manifolds with cusps which imply the existence of arbitrarily wide resonance free strips, local smoothing for the Schrodinger equation, and resonant wave expansions. We obtain lossless limiting absorption and local smoothing estimates, but the estimates on the holomorphically continued resolvent exhibit losses. We prove that these estimates are optimal in certain respects.