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On the Ornstein-Uhlenbeck operator in convex sets of Banach spaces (1503.02836v4)
Published 10 Mar 2015 in math.AP and math.FA
Abstract: 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 Poincar\'e inequalities, and thanks to these inequalities we deduce the spectral properties of the Ornstein-Uhlenbeck operator.
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