Geodesic
Asymptotic behavior of the invariant measure for a diffusion related to an $NA$ group
Ewa Damek 1   ; Andrzej Hulanicki 1
1 Institute of Mathematics Wrocław University Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
Colloquium Mathematicum, Tome 104 (2006) no. 2, pp. 285-309 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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

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