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Stochastic Dynamical Systems and Control |
| March 26, 2007 to March 30, 2007 |
| Organized By: Jonathan Mattingly (Duke), Igor Mezic (UCSB-Chair), Andrew Stuart (Warwick) |
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| Parent Programs: |
| Dynamical Systems |
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| Return to Workshop Description |
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Poisson spaces for proper semigroups of semi-simple Lie groups
Tuesday March 27, 2007
04:00PM - 04:30PM
Speakers:
Paulo Ruffino
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.
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