Characterizations of sets of finite perimeter using the Ornstein-Uhlenbeck semigroup in the Gauss space

The goal of this paper is to establish the relation between the notion of sets of finite perimeter and the theory of the Ornstein-Uhlenbeck semigroup in the setting of the Gauss space. We prove a characterization of sets of finite perimeter in terms of a short time behavior of the Ornstein-Uhlenbeck semigroup and we also give a new characterization of BV functions in terms of a near-diagonal energy in this space. (c) 2021 Elsevier Masson SAS. All rights reserved.