On the Ornstein-Uhlenbeck operator in convex sets of Banach spaces
نویسنده
چکیده
We study the Ornstein-Uhlenbeck operator and the Ornstein-Uhlenbeck semigroup in an open convex subset of an infinite dimensional separable Banach space X. This is done by finite dimensional approximation. In particular we prove Logarithmic-Sobolev and Poincaré inequalities, and thanks to these inequalities we deduce spectral properties of the OrnsteinUhlenbeck operator. 2010 Mathematics Subject Classification AMS 35R15, 39B62, 47D07
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