New sharp bounds for the Jacobi heat kernel via an extension of the Dijksma-Koornwinder formula

Abstract

We obtain sharp estimates for the Jacobi heat kernel in a range of parameters where the result has not been established before. This extends and completes an earlier result due to the authors. The proof is based on a generalization of the Dijksma-Koornwinder product formula for Jacobi polynomials.

17 pages