English

On the Ornstein-Uhlenbeck operator in convex sets of Banach spaces

Analysis of PDEs 2017-09-12 v4 Functional Analysis

Abstract

We study the Ornstein-Uhlenbeck operator and the Ornstein-Uhlenbeck semigroup in an open convex subset of an infinite dimensional separable Banach space XX. 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.

Keywords

Cite

@article{arxiv.1503.02836,
  title  = {On the Ornstein-Uhlenbeck operator in convex sets of Banach spaces},
  author = {Gianluca Cappa},
  journal= {arXiv preprint arXiv:1503.02836},
  year   = {2017}
}