Heat kernel estimates for a class of higher order operators on Lie groups

Nick Dungey¹

¹ School of Mathematics University of New South Wales Sydney 2052, Australia

Studia Mathematica, Tome 169 (2005) no. 1, pp. 71-80

Résumé

Let $G$ be a Lie group of polynomial volume growth. Consider a differential operator $H$ of order $2m$ on $G$ which is a sum of even powers of a generating list $A_1, \ldots, A_{d'}$ of right invariant vector fields. When $G$ is solvable, we obtain an algebraic condition on the list $A_1, \ldots, A_{d'}$ which is sufficient to ensure that the semigroup kernel of $H$ satisfies global Gaussian estimates for all times. For $G$ not necessarily solvable, we state an analytic condition on the list which is necessary and sufficient for global Gaussian estimates. Our results extend previously known results for nilpotent groups.

Détail

DOI : 10.4064/sm169-1-5

Keywords: lie group polynomial volume growth consider differential operator order which sum even powers generating list ldots right invariant vector fields solvable obtain algebraic condition list ldots which sufficient ensure semigroup kernel satisfies global gaussian estimates times necessarily solvable state analytic condition list which necessary sufficient global gaussian estimates results extend previously known results nilpotent groups