On Gaussian kernel estimates on groups

Schauder Estimates on Lie Groups

Geometric Inference on Kernel Density Estimates

We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and approximate computation in comparison to raw point sets. This is achieved by examining the sublevel sets of the kernel distance, which isomorphically map to s...

Heat kernel estimates on weighted graphs

We prove upper and lower heat kernel bounds for the Laplacian on weighted graphs which include the case that the weights have no strictly positive lower bound. Our estimates allow for a very explicit probabilistic interpretation and can be formulated in terms of a weighted metric. Interestingly, this metric is not equivalent to the intrinsic metric. The results Heat kernel estimates are a tool ...

A note on multivariate Gaussian estimates

Article history: Received 13 November 2008 Submitted by M. Peligrad

Precise Estimates for the Subelliptic Heat Kernel on H-type Groups

We establish precise upper and lower bounds for the subelliptic heat kernel on nilpotent Lie groups G of H-type. Specifically, we show that there exist positive constants C1, C2 and a polynomial correction function Qt on G such that C1Qte − d2 4t ≤ pt ≤ C2Qte d2 4t where pt is the heat kernel, and d the Carnot-Carathéodory distance on G. We also obtain similar bounds on the norm of its subellip...