Sharp estimates for the Jacobi and trigonometric Dunkl heat kernels

Abstract

We prove sharp both-sided estimates for the $W$-invariant trigonometric Dunkl heat kernel in rank one case, including root systems $A_1$ and $B{C}_1$. Consequently, we obtain sharp bounds for the non-compact Jacobi heat kernel in the full range of the type parameters.

arXiv comment21 pages