Geodesic
Asymptotic behavior of the invariant measure for a diffusion related to an $NA$ group
Ewa Damek1 ; Andrzej Hulanicki1
1 Institute of Mathematics Wrocław University Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
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 $S$.
DOI : 10.4064/cm104-2-6
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

Ewa Damek 1 ; Andrzej Hulanicki 1

1 Institute of Mathematics Wrocław University Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland 
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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. http://geodesic.mathdoc.fr/articles/10.4064/cm104-2-6/

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