
Journal of Lie Theory 23 (2013), No. 3, 655668 Copyright Heldermann Verlag 2013 Upper Bound for the Heat Kernel on HigherRank NA Groups Richard Penney Dept. of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907, U.S.A. rcp@math.purdue.edu Roman Urban Institute of Mathematics, Wroclaw University, Plac Grunwaldzki 2/4, 50384 Wroclaw, Poland urban@math.uni.wroc.pl [Abstractpdf] \def\R{{\Bbb R}} Let $S$ be a semidirect product $S=N\rtimes A$ where $N$ is a connected and simply connected, nonabelian, nilpotent metaabelian Lie group and $A$ is isomorphic with $\R^k,$ $k>1$. We consider a class of second order leftinvariant differential operators ${\cal L}_\alpha$, $\alpha\in\R^k$, on $S$. We obtain an upper bound for the heat kernel for ${\cal L}_\alpha$. Keywords: Heat kernel, left invariant differential operators, metaabelian nilpotent Lie groups, solvable Lie groups, homogeneous groups, higher rank $NA$ groups, Brownian motion, exponential functionals of Brownian motion. MSC: 43A85, 31B05, 22E25, 22E30, 60J25, 60J60 [ Fulltextpdf (327 KB)] for subscribers only. 