Sharp estimates for $W$-invariant Dunkl and heat kernels in the $A_n$ case

Abstract

In this article, we prove exact estimates for the $W$-invariant Dunkl kernel and heat kernel, for the root system of type $A$ with arbitrary positive multiplicities. We apply the estimates of the $W$-invariant Dunkl heat kernel to compute sharp estimates for the Newton kernel and for the $s$-stable semigroups generated by a fractional power of the $W$-invariant Dunkl Laplacian.

References in corpus (2)

• Sharp Estimates of Radial Dunkl and Heat Kernels in the Complex Case $A_n$
• Subordinated Markov processes: sharp estimates for heat kernels and Green functions