Characterization of BV functions on open domains: the Gaussian case and the general case
英文摘要：
We provide three different characterizations of the space $BV(O,γ)$ of the functions of bounded variation with respect to a centred non-degenerate Gaussian measure $ γ$ on open domains $O$ in Wiener spaces. Throughout these different characterizations we deduce a sufficient condition for belonging to $BV(O,γ)$ by means of the Ornstein-Uhlenbeck semigroup and we provide an explicit formula for one-dimensional sections of functions of bounded variation. Finally, we apply our technique to Fomin differentiable probability measures $ν$ on a Hilbert space $X$, inferring a characterization of the space $BV(O,ν)$ of the functions of bounded variation with respect to $ν$ on open domains $O\subseteq X$.
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