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On the Ornstein–Uhlenbeck operator in convex subsets of Banach spaces

Volume 247 / 2019

Gianluca Cappa Studia Mathematica 247 (2019), 217-239 MSC: 35R15, 39B62, 47D07. DOI: 10.4064/sm8229-3-2018 Published online: 25 January 2019


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.


  • Gianluca CappaDepartment of Economics and Finance
    LUISS Guido Carli University
    Viale Romania 32
    00197 Roma, Italy

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