论文标题
部分可观测时空混沌系统的无模型预测
Optimal heat kernel bounds and asymptotics on Damek--Ricci spaces
论文作者
论文摘要
我们为Laplace-Beltrami操作员在Damek-ricci空间上的热内核的径向，时空和时间衍生物提供了最佳界限。在等级第一的对称空间的情况下，这些完整且实际改善了Anker和JI的猜想估计。我们还提供了无限元的无限范围的渐近和时间衍生物的渐变性。一路上，我们为Riemannian距离的所有衍生物提供了尖锐的边界，并为杰出的Laplacian的热核的界限提供了类似的边界。
We give optimal bounds for the radial, space and time derivatives of arbitrary order of the heat kernel of the Laplace--Beltrami operator on Damek--Ricci spaces. In the case of symmetric spaces of rank one, these complete and actually improve conjectured estimates by Anker and Ji. We also provide asymptotics at infinity of all the radial and time derivates of the kernel. Along the way, we provide sharp bounds for all the derivatives of the Riemannian distance and obtain analogous bounds for those of the heat kernel of the distinguished Laplacian.
