Geodesic
Sub-Laplacian with drift in nilpotent Lie groups
Camillo Melzi1
1 Dipartimento di Scienze Chimiche, Fisiche e Matematiche Università degli studi dell'Insubria via Valleggio 11, 22100 Como, Italy
Colloquium Mathematicum, Tome 96 (2003) no. 1, pp. 41-53

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider the heat kernel $\phi _t$ corresponding to the left invariant sub-Laplacian with drift term in the first commutator of the Lie algebra, on a nilpotent Lie group. We improve the results obtained by G. Alexopoulos in [1], [2] proving the “exact Gaussian factor” $\mathop {\rm exp}\nolimits \left (-{| g| ^2\over 4(1+\varepsilon )t} \right)$ in the large time upper Gaussian estimate for $\phi _t$. We also obtain a large time lower Gaussian estimate for $\phi _t$.
DOI : 10.4064/cm96-1-5
Keywords: consider heat kernel phi corresponding invariant sub laplacian drift term first commutator lie algebra nilpotent lie group improve results obtained alexopoulos proving exact gaussian factor mathop exp nolimits varepsilon right large time upper gaussian estimate phi obtain large time lower gaussian estimate phi

Camillo Melzi 1

1 Dipartimento di Scienze Chimiche, Fisiche e Matematiche Università degli studi dell'Insubria via Valleggio 11, 22100 Como, Italy 
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Camillo Melzi. Sub-Laplacian with drift in nilpotent Lie groups. Colloquium Mathematicum, Tome 96 (2003) no. 1, pp. 41-53. doi: 10.4064/cm96-1-5

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