Gaussian bounds for the heat kernels on the ball and simplex: Classical approach

TL;DR

This paper establishes two-sided Gaussian bounds for heat kernels on the unit ball and simplex in , using classical differential operators with polynomial eigenfunctions, advancing understanding of heat kernel behavior in these domains.

Contribution

It provides new Gaussian bounds for heat kernels on the ball and simplex, employing classical differential operators with polynomial eigenfunctions.

Findings

Two-sided Gaussian bounds for heat kernels on the ball and simplex.

Bounds are derived for kernels generated by classical differential operators.

Results enhance understanding of heat kernel estimates in geometric domains.

Abstract

Two-sided Gaussian bounds are established for the weighted heat kernels on the unit ball and simplex in $\mathbb{R}^d$ generated by classical differential operators whose eigenfunctions are algebraic polynomials.