Poisson Spaces for Proper Semigroups of Semi-simple Lie Groups
Stochastic Dynamical Systems and Control
March 27, 2007 04:00 PM to 04:30 PM
Speakers:
Ruffino, Paulo
|
 |
Abstract: |
Let \nu be a probability measure on a semi-simple Lie group $G$ with
finite center. Under the hypothesis that the semigroup $S$ generated by
\nu has non-empty interior, we identify the Poisson space \Pi
=G/M_{\nu }AN, where bounded (l.u.c.) \nu -harmonic functions in G
have a
one-to-one correspondence with measurable (continuous) functions in \Pi
. This article extends a classical result (see Furstenberg,
Azencott Azencott and others), where the semigroup generated by
\nu was assumed to be the whole (connected) group. We present two
detailed examples. |
|
|
