Heat kernels of metric trees and applications
Spectral Theory
2011-09-02 v1 Mathematical Physics
math.MP
Abstract
We consider the heat semi-group generated by the Laplace operator on metric trees. Among our results we show how the behavior of the associated heat kernel depends on the geometry of the tree. As applications we establish new eigenvalue estimates for Schroedinger operators on metric trees.
Cite
@article{arxiv.1108.6145,
title = {Heat kernels of metric trees and applications},
author = {Rupert L. Frank and Hynek Kovarik},
journal= {arXiv preprint arXiv:1108.6145},
year = {2011}
}