Asymptotic behavior of the invariant measure
for a diffusion related to an $NA$ group
Colloquium Mathematicum, Tome 104 (2006) no. 2, pp. 285-309
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
On a Lie group $NA$ that is a split extension of a nilpotent Lie group $N$ by a one-parameter group of automorphisms $A$, the heat semigroup $\mu _t$ generated by a second order subelliptic left-invariant operator $\sum _{j=0}^mY_j +Y$ is considered. Under natural conditions there is a
$\check \mu _t$-invariant measure $m$ on $N$, i.e. $\check \mu _t*m=m$. Precise asymptotics of $m$ at infinity is given for a large class of operators with $Y_0,\dots,Y_m$ generating the Lie algebra of $S$.
Keywords:
lie group split extension nilpotent lie group one parameter group automorphisms heat semigroup generated second order subelliptic left invariant operator sum considered under natural conditions there check t invariant measure check t*m precise asymptotics infinity given large class operators dots generating lie algebra
Affiliations des auteurs :
Ewa Damek 1 ; Andrzej Hulanicki 1
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author = {Ewa Damek and Andrzej Hulanicki},
title = {Asymptotic behavior of the invariant measure
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journal = {Colloquium Mathematicum},
pages = {285--309},
publisher = {mathdoc},
volume = {104},
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year = {2006},
doi = {10.4064/cm104-2-6},
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Ewa Damek; Andrzej Hulanicki. Asymptotic behavior of the invariant measure for a diffusion related to an $NA$ group. Colloquium Mathematicum, Tome 104 (2006) no. 2, pp. 285-309. doi: 10.4064/cm104-2-6
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