论文标题
Schrödinger操作员在产品锥上的分散估计值
Pointwise dispersive estimates for Schrödinger operators on product cones
论文作者
论文摘要
我们研究了Schrödinger方程的溶液的分散性能，其圆锥上的径向电势较弱。如果电势在无穷大时具有足够的多项式衰减，那么我们表明，链接歧管的每个特征空间上的schrödinger流都满足加权的$ l^1 \ to l^\ infty $分散估计。在奇数尺寸中，我们计算的衰减速率与同一维度的欧几里得空间中的schrödinger方程相一致，但是空间重量反映了我们以光谱度量的形式面对的频率中更复杂的规律性问题。在什至维度上，我们证明了类似的估计，但是与尖锐的欧几里得估计相比，$ t^{1/2} $损失。
We investigate the dispersive properties of solutions to the Schrödinger equation with a weakly decaying radial potential on cones. If the potential has sufficient polynomial decay at infinity, then we show that the Schrödinger flow on each eigenspace of the link manifold satisfies a weighted $L^1\to L^\infty$ dispersive estimate. In odd dimensions, the decay rate we compute is consistent with that of the Schrödinger equation in a Euclidean space of the same dimension, but the spatial weights reflect the more complicated regularity issues in frequency that we face in the form of the spectral measure. In even dimensions, we prove a similar estimate, but with a loss of $t^{1/2}$ compared to the sharp Euclidean estimate.
