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

Volume 169 / 2005

Nick Dungey Studia Mathematica 169 (2005), 71-80 MSC: 22E30, 22E25, 35B40. DOI: 10.4064/sm169-1-5


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.


  • Nick DungeySchool of Mathematics
    University of New South Wales
    Sydney 2052, Australia

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