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Invariant measure for some differential operators and unitarizing measure for the representation of a Lie group. Examples in finite dimension. (English) Zbl 1260.60157

Bożejko, Marek (ed.) et al., Noncommutative harmonic analysis with applications to probability. III: Papers presented at the 13th workshop, Bȩdlewo, Poland, July 11–17, 2010. Warszawa: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-15-7/pbk). Banach Center Publications 96, 9-34 (2012).
The following concepts are defined: unitarizing measure for the representation of a Lie group in a space of holomorphic functions; infinitesimal representation of the Lie algebra; construction of the Ornstein-Uhlenbeck operator with a drift term and real valued coefficients. The problem, when the group representation measure is an invariant measure is investigated.
For the entire collection see [Zbl 1248.46002].

MSC:

60J60 Diffusion processes
60H07 Stochastic calculus of variations and the Malliavin calculus
58J65 Diffusion processes and stochastic analysis on manifolds
35R03 PDEs on Heisenberg groups, Lie groups, Carnot groups, etc.
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