Journal of Lie Theory

no. 3
Upper Bound for the Heat Kernel on Higher-Rank NA Groups
Journal of Lie Theory, Volume 23 (2013) no. 3, pp. 655-668
\def\R{{\Bbb R}} Let $S$ be a semi-direct product $S=N\rtimes A$ where $N$ is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and $A$ is isomorphic with $\R^k,$ $k>1$. We consider a class of second order left-invariant differential operators ${\cal L}_\alpha$, $\alpha\in\R^k$, on $S$. We obtain an upper bound for the heat kernel for ${\cal L}_\alpha$.
DOI: 10.5802/jolt.742
Classification: 43A85, 31B05, 22E25, 22E30, 60J25, 60J60
Keywords: Heat kernel, left invariant differential operators, meta-abelian nilpotent Lie groups, solvable Lie groups, homogeneous groups, higher rank $NA$ groups, Brownian motion, exponential functionals of Brownian motion 
@article{JOLT_2013_23_3_a2,
     author = {R. Penney and R. Urban},
     title = {Upper {Bound} for the {Heat} {Kernel} on {Higher-Rank} {NA} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {655--668},
     year = {2013},
     volume = {23},
     number = {3},
     doi = {10.5802/jolt.742},
     zbl = {1279.43013},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.742/}
}
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%A R. Urban
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R. Penney; R. Urban. Upper Bound for the Heat Kernel on Higher-Rank NA Groups. Journal of Lie Theory, Volume 23 (2013) no. 3, pp. 655-668. doi: 10.5802/jolt.742

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