Genuinely sharp estimates for heat kernels on Weyl chambers

Abstract

We consider heat kernels on Weyl chambers corresponding to Laplacians subject to mixed Dirichlet-Neumann boundary conditions imposed on the boundary. Using purely analytic tools we prove genuinely sharp two-sided global estimates in the frameworks of orthogonal root systems and the dihedral root systems $I_2(3)$ and $I_2(4)$.

arXiv comment35 pages, 2 figure

References in corpus (2)

• Sharp estimates of the spherical heat kernel
• Reflection principles for functions of Neumann and Dirichlet Laplacians on open reflection invariant subsets of ${\mathbb{R}}^d$