On the Ornstein–Uhlenbeck operator in convex subsets of Banach spaces
Volume 247 / 2019
Studia Mathematica 247 (2019), 217-239
MSC: 35R15, 39B62, 47D07.
DOI: 10.4064/sm8229-3-2018
Published online: 25 January 2019
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 Poincaré inequalities, and thanks to these inequalities we deduce spectral properties of the Ornstein–Uhlenbeck operator.
